Peter Gojowczyk sits 161 places below world number 48 Nicolas Almagro and failed to convert match point in a tense second set, with the Spaniard finally managing to force a decider at the seventh attempt.
The German quickly moved a break up in the third set and never looked back, with another big test in Dominic Thiem awaiting him in the second round.
Seventh seed Benoit Paire was defeated by fellow Frenchman and qualifier Vincent Millot 6-4 6-3, while Dustin Brown overcame another home hope in Paul-Henri Mathieu 6-4 6-2.
Nikoloz Basilashvili and Guillermo Garcia-Lopez produced impressive displays to come from behind and advance.
Georgian Basilashvili defeated Gregoire Barrere 5-7 7-5 6-2 to set up a match against Gilles Muller in the last 16, while Gilles Simon is next up for Garcia-Lopez, who bested Damir Dzumhur 5-7 6-2 6-1.