The match proved to be a tight and tense affair between the two good friends, with Sweeting prevailing 7-5 in an opening set tie-break.
The 118th ranked player then saved five break points in the second set, and secured the crucial break himself to take the second set 6-4.
Wild card James Blake exited the tournament as he was beaten 6-3 6-4 by Japan's Kei Nishikori in a rematch of the 2009 final.
Janko Tipsarevic beat Blaz Kavcic 6-2 6-7 (8/10) 6-3 while, in a first-round contest, eighth seed Adrian Mannarino was a 1-6 7-6 (7/3) 6-4 victor over Leonardo Mayer.