Alves set up Mario Mandzukic's opener in the 33rd minute and got on the scoresheet himself on the stroke of halftime with a fantastic volley as Juventus swept to a 4-1 victory on aggregate.
It was a fantastic performance from the 34-year-old wing back, who many described as being past his best when he joined from Barcelona on a free transfer in the offseason.
"Three months ago, some people wanted to strangle Dani Alves," Juventus coach Massimiliano Allegri said with a smile.
Kylian Mbappe scored a consolation goal in the 69th minute for Monaco, as Juventus remained on course for the treble.
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Allegri's side is likely to secure an unprecedented sixth Serie A title on Sunday at Roma, while it is also in the Italian Cup final.
Two years ago, Juventus was in a similar position but it lost the final 3-1 to Barcelona. This time, it could be Juve's year, especially after it eased past the Catalan team 3-0 on aggregate in the quarterfinals.
Juventus will be attempting to end a 21-year wait for a European trophy.
"It's a path that started a long time ago," Allegri said.
"Everyone has grown: the club, the players, myself. Have to compliment everyone. From tomorrow we have to think about what we can do in these in 20 days.
"It's right to be enthusiastic, but we'll take it one step at a time. We have to improve certain things, because this squad is capable of improving."
"We leave here eliminated, but still with our heads held high," Mbappe said. "My goal against Buffon didn't help anything, it's pretty much just anecdotal."
As for Monaco's performances in this season's Champions League, Mbappe saw them as valuable experience.
"We had a good run ... We don't have many regrets about this European campaign," he said. "Mixing with the top teams is what's best for progression. Today we learnt a lot, I learnt a lot and we'll try to come back next season better armed."
Juventus soaked up the early pressure before stepping up a gear midway through the half. Gonzalo Higuain burst into the area and chipped Monaco goalkeeper Danijel Subasic, but defender Kamil Glik hooked the ball clear.
Subasic then did well to deny Mandzukic, who also sent a header wide shortly afterward as Juventus pushed for the goal which would effectively end the contest.
Juventus doubled its tally just before halftime. Subasic punched clear a corner but it fell to Alves, who volleyed it into the back of the net from outside the area.
Monaco scored when a corner was played short and Joao Moutinho put in a low cross for Mbappe to fire home from close range.