The powerful hitting of Zverev was taking its toll on the four-time champion, but he was able to cope well as the second set was moving along routinely, service games competitive, but no breaks or break points achieved by either player.
Zverev, with a stinging forehand victor backed up by several strong serves, allowed him to open an early lead in the tiebreak.
The first week back on the ATP World Tour after the Australian Open and Davis Cup has seen Alexander Zverev, Grigor Dimitrov and Victor Estrella Burgos claim titles.
It was very much Alexander Zverev's day in Montpellier, where he claimed two titles.
He then broke Gasquet again to lead 5-3 in the second set and held his serve to win the crown.
The fourth-seeded Zverev was solid against the third-seeded Gasquet, winning 80 percent of his points on first serve and hitting eight aces. The indoor showpiece has former US Open victor Marin Cilic as top seed, with the 2014 finalist starting the latest edition against quirky Frenchman Benoit Paire on Tuesday.
"He broke me quickly at the beginning of the match. He deserves his victory".
Krajicek said the presence of highly-rated German teenager Zverev and Bulgarian Dimitrov was a stroke of fortune.
Dimitrov gave another indication that he is ready to make further strides this season by beating David Goffin 7-5 6-4. We only dropped one set in the tournament.