Opening batter Evans, who replaced the injured Jos Buttler as captain of the Originals, got his side off to a flier in response to Spirit's 150, with a 101-run stand with Phil Salt.
But a wobble led by Mason Crane (two for 35) and Nathan Ellis (two for 31) gave Eoin Morgan's men hope before Ashton Turner and Tom Lammonby got Originals over the line with 11 balls to spare.
Originals will now face Trent Rockets at Lord's in Saturday's final.
Speaking after the match, Manchester Originals skipper Laurie Evans told Sky Sports: "I would have enjoyed the win a lot more if I had finished the job off [myself] but it is amazing to get over the line. The team have been incredible all the way through. Six wins in a row and now we go again.
"There is no secret to this success - just good blokes, playing good cricket and working hard for each other. It has been so enjoyable to be a part of.
"I have never really experienced a group of guys who like playing together as much as this. The story of our campaign has been different guys stepping up at different times.
"Trent Rockets have been fantastic all the way through. All the pressure will be on them to win this tournament because they have been the best team. We are just going to try and cause an upset."