Kiwi Bevin took the leader's green jersey thanks to six bonus seconds snatched on the finish line and Australia's Cameron Meyer retained second place.
"I'm really really happy - like always when we win - but especially today because we tried since start of the race and today we knew it was a good opportunity," said Alaphilippe, who moved up to third in the overall standings.
"The team did a great job all day, they controlled the race - especially the finale With Bob we were together trying to attack or maybe sprint with me and in the end he did a perfect lead-out. I was also really happy to finish the job of my team with a nice victory."
Team Sky's Wout Poels finished 15th to stand fifth overall, 12 seconds behind race leader Bevin.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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