The unseeded Croat fired 16 aces and saved nine of 10 break points to claim his second victory over Becker this season.
Eighth seeded Juan Monaco of Argentina, seeking his second ATP victory of the season, beat American wild card Jan-Michael Gambill 7-5 6-4.
Monaco told reporters that the match had been difficult but that he gained confidence and power as it progressed.
Romanian Victor Hanescu snapped a 12-match losing streak by defeating Dutchman Martin Verkerk 6-4 6-4 to record his first ATP-level victory in more than a year.
Frenchman Nicolas Devilder converted four of 13 break opportunities to top American wild card Justin Gimelstob 6-2 6-3.
Three-times Houston champion Andy Roddick withdrew from the field on Monday after aggravating a hamstring injury while leading the U.S. past Spain in the Davis Cup over the weekend.
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