Davis Cup Tennis GB v Russia
World number 214 Ward beat former Davis Cup winner Dmitry Tursunov 6-4 5-7 5-7 6-4 6-4 to level the Euro/Africa Group One tie after GB trailed 2-1 overnight.
Evans, world number 325, then shocked Evgeny Donskoy, ranked 245 places higher, 6-4 6-4 6-1 as Britain clinched a place in the World Group play-offs.
AnalysisRussell Fuller BBC Radio 5 live at Coventry's Ricoh Arena
"James Ward showed huge courage to complete such a high-class victory after losing so painfully on Friday night, in what he says has not been an easy week for him personally. And Dan Evans made a mockery of his ranking - he looked like he was born for the moment. Captain Leon Smith deserves a huge amount of credit for picking the British number six and for coaxing the best out of his underdogs. This was a fantastic team effort and with Andy Murray promising to make himself available in September, a return to the World Group may be on the cards."
It is the first time since 1930 that Britain have won from trailing 2-0.
Two-time winners Russia were relegated from the World Group last year for the first time in 20 years and, with British number one Andy Murray opting to miss the tie, went in as clear favourites at the Ricoh Arena.
Ward recovered from two sets to one down to win a five-set marathon against world number 67 Tursunov and send the tie into a decisive rubber.
The British player, who lost a marathon match to Donskoy on the opening day of the tie, put the win over Tursunov up alongside his first-round Wimbledon victory over Spain's Pablo Andujar last year as the best of his life.
"This has to be one of the sweetest victories of my career, after injuries last year and coming so close to winning on Friday, winning this in five is a big achievement for me, " he said.
"It's got to up to there as one or two. Wimbledon's always special because it's the biggest tournament in the world. [Andujar] was a top-30 player as well so that was special but this is just as much.
"I was two sets to one down against a guy who's been 20 in the world. If anything, it's even more pleasing beating Tursunov. He's been a bit of a bogey man for me."
Great Britain 3-2 Russia
- Friday: Tursunov bt Evans 6-4 6-7 (5-7) 6-4 5-7 6-4
- Friday: Donskoy bt Ward 4-6 4-6 7-5 6-2 8-6
- Saturday: Fleming & Marray bt Kunitsyn & Baluda 6-1 6-4 6-2
- Sunday: Ward bt Tursunov 6-4 5-7 5-7 6-4 6-4
- Sunday: Evans bt Donskoy 6-4 6-4 6-1
That set the stage for Evans, who was the hero of Britain's victory over Slovakia last year, to record an emphatic straight-sets win inside two hours.
Evans said: "I expected to have to do quite a lot more running than I did and it was quite surprising how the match went, I think for both of us. But obviously I was really happy with that and I played really well.
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