Gasquet struggled to return serves in the first set but recovered to wrap up the match with a backhand winner after 2 hours, 6 minutes. Gasquet will next face either Jarkko Nieminen or Florent Serra.
Gasquet served 11 aces and broke his opponent four times while Reister converted only one of his five break chances.
In the first-set tiebreaker, Gasquet had set point at 8-7 up on Reister's serve, but the German won the next three points.
Gasquet then lost his serve right at the start of the second set - having not faced a single break point in the first set. But he broke straight back and then held easily to make it 2-1.
Gasquet had two break points for a 4-2 lead but Reister saved both before faltering in his next service game, where he was broken to love.
Frederico Gil of Portugal beat Edouard-Roger Vasselin of France 6-4, 2-6, 7-5 to advance.
Both players struggled for consistency and lost serve four times each on the indoor hard court. Gil also saved a further nine break points.
The 100th-ranked Gil, who lost his only career final this year to Albert Montanes of Spain on clay on home soil at Estoril, next plays France's second seeded Jo-Wilfried Tsonga, who had a bye to the second round.
Later Monday, the sixth-seeded Montanes was to play Arnaud Clement of France.
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