Alves provided the cross for Mario Mandzukic to score the first goal in the semi-final, second leg and then added the second himself with an explosive strike to effectively finish off the tie by halftime.
Juventus, who had won the first leg 2-0, were coasting until Kylian Mbappe pulled one back in the 69th minute, ending a run of six successive clean sheets in the competition for the Serie A side and veteran goalkeeper Gianluigi Buffon.
Tempers then flared when Monaco defender Kamil Glik appeared to stamp on Juventus forward Gonzalo Higuain, although the referee took no action against the Pole, leading to a bad-tempered final 20 minutes.
Juventus, who ran out 4-1 aggregate winners, will face either Real Madrid or Atletico Madrid, who meet in the other semi-final on Wednesday. The final is in Cardiff on June 3.
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