The former New Zealand fly-half converted wing Gonzalo Camacho's 76th-minute try at Cardiff City Stadium as Quins stunned French giants Stade Francais 19-18 to lift the Amlin Challenge Cup.
Stade looked to have dome enough through four Lionel Beauxis penalties and drop-goals from centre Mathieu Bastareaud and full-back Martin Rodriguez.
But Quins conjured a special finish as prop Joe Marler and scrum-half Danny Care completed the hard yards for Camacho to cross and hand Evans his match-winning chance.
Evans said: "All those times on the training pitch you dream of moments like that one. I was excited to have the kick - I wasn't nervous. That is what we live for as kickers.
"Credit to the whole team. We never gave up, and I think we have shown that throughout the season. We got ourselves out of jail, got the win and got the silverware.
"I enjoy it with Quins, that's why I signed for another couple of years.
"I heard Sir Alex Ferguson say the other day that winning the first trophy is the toughest with a group of players. Hopefully now, we can push on and create a bit of a dynasty."
Evans earlier kicked four penalties for a 14-point haul, and Stade now need Northampton to win Saturday's Heineken final against Irish favourites Leinster in the Welsh capital.
If Saints topple the favourites and become England's first European champions since 2007, then Stade will join Quins in Heineken action next term.
But a Leinster triumph would leave Stade floundering and send Irish province Connacht through instead.
Quins rugby director Conor O'Shea said: "We didn't play well.
"We've lost some pretty heartbreaking games this season, but my wife always said to me we would get some luck at the end of the year, and we did. We hung on in there and never gave up.
"Across the pitch, we didn't have the greatest of games, but we kept on playing and trying - that's the motto of the team.
"It might be Gonzalo's last game for the club, but if it is, what an incredible to way sign off. I thought he was magnificent throughout the game."
Stade struggled to contain their emotions at the end, with captain Sergio Parisse attempting to make his feelings known to Irish referee George Clancy.
And the Parisians' head coach - former Leinster boss Michael Cheika - did not hold back in his post-match press conference.
"We are pretty devastated," he said. "We deserved a lot better, I think.
"Once again we came undone due to the shortcomings of, you know. I don't think I should say it because I will only get in trouble.
"We are very disappointed. We made some small mistakes which Harlequins were very good at taking advantage of, some snippets of the game when they got through us."
Stade were penalised at a late scrum as they tried to establish field position and rescue the game, but Cheika added: "That, unfortunately, was a joke (being penalised at the scrum). We pushed them off the ball.
"The areas where we dominated in the second half, the referee took our advantage away. It's a shame.
"Sergio was a bit upset at the end. I went to take the player away from him (Clancy) to help him, and he carried on with fear. He didn't want to explain to me, he didn't want to do anything.
"It's big stakes. We deserved to win, and I hope it is not perceived as just sour grapes. I am trying to be as measured as I can - I thought we played very well."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.