The Latvian emerged victorious from a grueling hour-long final set to win the tie-break 12-10 and seal a 7-6 7-5 7-6 victory over the battling Zopp.
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Nothing could separate the duo in the opening set as a solid service game from both led to the pair claiming six games apiece.
Gulbis started the tie-break in woeful fashion, surrendering a three-point lead early on, but the 25-year-old recovered to claim a first-set win by a 9-7 victory.
The second set began in similar fashion as the pair held their serve en route to being deadlocked at five games apiece again, but something gave when Zopp lost his service game for the first time in the match and Gulbis pounced to earn a 7-5 win.
Despite trailing by two sets, Zopp refused to go quietly and ensured that Gulbis would have to earn his place in the second round as the third set went the same way as the previous two.
Deadlocked at 6-6, the close proximity between the duo remained throughout a thrilling third-set tie-break, with both players claiming 10 points apiece.
However, Gulbis moved one away from victory before inflicting a crucial break of serve in the final point to win the two-and-a-half hour encounter and get his Wimbledon campaign off to a strong start.