The world number 39 became the first player at the tournament to take a set off the Spaniard, racing out to a 3-0 lead in the second set which he eventually won after having to save match point.
The British number two was eventually outlasted 7-5 6-7 6-2 across two hours and 58 minutes by Carreno Busta, with the pair appearing exhausted as they embraced at the net as the match ended.
The 23rd-ranked Carreno Busta relied on his first serve to dominate his opponent, recording 43 winners and breaking on five of his eight chances.
The victory pushes the Spaniard through to his first ATP Masters final, which will be against eighth-seeded Hubert Hurkacz after the Pole earlier dropped his first set before fighting back to defeat Casper Ruud.
Evans’ strong recent showings should see him surge up the rankings to the edge of the top 20, with those ranked 32 and higher seeded for the upcoming US Open.
The 32-year-old will next play Filip Krajinovic in the first round of the Western and Southern Open, the final warm-up tournament before Flushing Meadows.