The League Two promotion chasers grabbed two late goals to seal a brilliant 2-1 third-round comeback victory at Villa Park.
Dean Campbell’s 90th-minute winner came just two minutes after Jamie Reid levelled from the spot, Leander Dendoncker having been sent off for fouling Campbell in the box.
It was an embarrassing exit for Villa, who had taken a first-half lead through Morgan Sanson, and Stevenage’s victory comes exactly 12 years after they also knocked Newcastle out in the third round.
“I’ve got grandkids, little Joseph, James and Mimi will be hearing about in the next few years,” said Evans after booking a fourth round trip to Stoke.
“I’ve had some magical moments, I’ve been in charge of lots of wins over Championship clubs but if you come away to a Premier League club like Aston Villa…it’s up there with them.
“It’s magical for the players, the chairman and for the town of Stevenage to see over 3,000 fans and winning the way we did, it’s the FA Cup and what dreams are made of.
“I said to the players they will have a dream they will talk to the kids and grandkids about.
“We stayed in the game and the plan all week was make sure we were in the game at 75 minutes. If we were in the game at 75 minutes I knew we had an incredibly fit group and I could use the lads who have hearts the size of Big Ben.”
Villa struggled to assert any authority against well-drilled Stevenage and the visitors thought they had taken the lead after 17 minutes when Danny Rose converted Luke Norris’ cross, only for the offside flag to cut short celebrations.
The hosts were one-paced but did conjure one piece of quality in the first half to create the opener when Philippe Coutinho, Leon Bailey and Danny Ings combined to tee up Sanson to drill in.
Norris clipped the bar in response but Villa’s opener should have provided the platform for victory yet a combination of resolute defending and poor finishing kept Stevenage in the game.
Calum Chambers prodded wide and Bailey’s wayward finishing continued before a stunning finale.
With five minutes left Robin Olsen found Dendoncker on the edge of his own box and he was immediately closed down by Campbell.
The midfielder dragged him back and, after referee Graham Scott initially gave a free-kick, he awarded a penalty and sent the midfielder off.
Reid buried the spot kick and, two minutes later, Stevenage completed their dramatic comeback. Villa switched off from a short corner with Campbell allowed to advance and beat Olsen at his near post.
“We have to continue the process, be very demanding like I was but maybe more now,” said boss Unai Emery.
“Each match is giving us more information. I want to work with the players, I want to create a bigger mentality. Sometimes it (losing) could be the first step.
“We can’t think we are better and we are Aston Villa and they are in League Two. I am upset, disappointed, I’m sorry for our supporters.
“When they score the last five minutes we were upset and didn’t control our minds. I know sometimes we have to lose and to take mistakes. We have to use it to learn as soon as possible thinking we can create a new way.”