Not to take a deep dive into this, but..

They may be credited for "saving" DC by some, but after the late 70s implosion, a number of corrective measures were being taken, and strong creative teams either continued or were assigned to long-running titles that began to catch new heat independent of the Perez/Wolfman success with The New Teen Titans. For example, at the end of the 70s, The Legion of Super-Heroes was still marching along under the Conway/Staton team. While not creating fan lines around the block, the title survived the implosion and soldiered on, right into the period where DC had changed its fortunes, with its "The New DC - Where the Action Keeps On Coming!" house ads, which appeared around August of 1981. Yes, by that time, the Perez/Wolfman revolution was on the march, but a title like the LSH moved into a brief Roy Thomas period, then what I would describe as the next big creative explosion for the title since the Bates/Cockrum/Grell days, in the hands of Levitz/Giffen. The rest, as they say, is

Now, i could be argued that other successes might have benefited from Wolfman as editor, such as the case after DC wisely obtained the rights to adapt the movie era of Star Trek. Making its debut in February of 1984, Star Trek comic was riding a rather massive wave after 1982's Star Trek II - The Wrath of Khan became a game-changing hit which saved the ST franchise.

Beginning publication five months before the highly anticipated sequel, Star Trek III - The Search for Spock hit theatres, DC's trip to the Final Frontier was--to my memory--a success, largely thanks to the series being credited for being the first to actually "get" the essence of Star Trek (certainly more than Marvel's then-recent disaster), with talents such as Mike W. Barr & Tom Sutton at the helm. If that was not enough, the title earned a wealth of ST-fan credibility by having Diane Duane (author of Pocket Books' 1983 Star Trek novel, The Wounded Sky) contribute scripts. How much Wolfman had an impact on the title (plus, he would occasionally co-edit with Barr) requires more research, but I think ST's healthy 4-year run was--in part--due to many progressive decisions DC made at the end of the previous decade, and cannot all be placed at the feet of one team, no matter how revolutionary they were, and I say this as one of the biggest Wolfman/Perez fans you're likely to find anywhere.

Which is a bit surprising given Marvel's reputation as flying by the seat of its pants (Jim Shooter notwithstanding) while DC was allegedly full of stuffy business types who wore jackets and ties as they labored at their art boards.

They definitely did get it up and running again as a relevant comic company but I'd think John Byrne may have had more to do with bringing DC back from the dead. 

I will echo this, and add Paul levitz and Dick Giordano.  It started with Kahn, taking over as publisher, and adding the professionalism of her higher profile publishing background.  She worked with Scholastic, publishing their Dynamite magazine, which was an excellent publication (available through their school book order program).  She had the smarts and started making the place more conducive to compensating the creative people more fairly, which attracted creators and got some of the existing talent to up their game, since the reward was better.  She got some advice from neal Adams, according to Jacobs & Jones The Comic Book Heroes.  Levitz brought the fan perspective, solid writing credentials and a business degree, which made him a great number two.  Giordano became Managing Editor in 1981 and really did a lot to set editorial on the right path, as well as creative relations.

The start of things though is 78-79.  Kahn took over in 1976; but, spent quite a bit of time both getting up to speed and fighting with entrenched management.  Levitz was one of her first allies, with Giordano recruited later.  Sol Harrison was president, when she took over and fought her tooth and nail, up to his retirement, in 1981.  She implemented a lot of experiments with formats (the Dollar Comics, for instance) and pushed to improve both packaging and content.  It took time to pay off; but, the machinery was running when Wolfman and Perez came in.  Their commercial success with New Teen Titans did a lot to elevate DC's profile and improve their bottom line; but, their sales had been on an upward swing, through 1979.  Wolfman and Perez are more an end result of what was put in motion when Kahn came in, in 1976.

These kinds of things are always an evolution, with many contributing factor.  To say one comic saved things is a bit much.  It was a very strong component; but, not a singular thing, any more than Star Wars "saved Marvel."  It was a massive financial success, that fueled their coffers; but, they weren't on death's door.  The market was bad in the mid-70s (for all publishing, not just comics); but, not that bad.  DC made more money off of licensing, which was already strong, when Kahn took over and got a massive shot in the arm with the release of the Donner Superman, in 1978.  They weren't going anywhere, because licensing earned them more than enough to offset their publishing losses.  That is also why I take the Shooter story about Marvel being approached about publishing DC with a big grain of salt.  He has been the only reference to this story and, at best, it sounds like some Warner person investigating the possibility of cheaper publishing and probably had no involvement with any DC execs, which I would bet would create a turf war, within Warner.  Wouldn't be surprised if it had been something initiated by someone looking to gain points within Warner, who got slapped down (just a hunch).

DC's revival was a gradual thing.  Kahn comes in in 76, Levitz is in editorial by 78 and is tapped as an ally to Kahn.  Experimentation in 79 and 79 leads to an expansion and quick restriction of the line; but, also some experiments in formats that prove promising.  Giordano comes onboard in 1980, Wolfman & Perez come over from Marvel (Englehart and Conway were already around) and Warlord has been selling well for DC; Superman movie in 78 gives DC a mainstream profile boost and big licensing revenue.  Entrenched management is mostly gone by 1981 and new blood is pushing experimentation, as well as recruitment of disaffected Marvel people.  NTT and Warlord are joined by Legion of Superheroes and Firestorm, as successful titles; experiments in mini-series and the Camelot 3000 maxi series is a test of the Direct Market distribution system.  That leads to further Direct only titles, which prove more profitable, with more focused print runs.  Things continue to improve through 192-84 and planning is put in place for the 50th anniversary, in 1985, with Crisis the end result.  DC experiments with graphic novels and higher quality limited projects, like Frank Miller's Ronin.  1986 sees post-Crisis relaunches and Dark Knight, followed by watchmen and the Byrne Superan revamp, plus Batman year One and the relaunch of Wonder Woman.  All steps along a path.  None occurs in a vacuum.

Alan Moore's Swamp Thing and the Crisis on Infinite Earths preceded Byrnes arrival. I thought they were rolling along before 1986.

Thank you. Very hard to get Back Issue here (I should put in an order), doesn't seem to reach these shores much (at least not in my area).

EDIT: Thanks again, what a great cover. I am sure she had a lot to say.