Venus sets up second-rounder with Kvitova in Doha
Williams was broken only once, when she led Martic 4-0.
She has an up and down record so far this season, reaching the final in Auckland and losing in the first round at the Australian Open. Williams has won only one of her three matches against Kvitova, the third seed who has a first-round bye, but all three have gone the distance.
Also, China's Peng Shuai beat 2006 champion Nadia Petrova 7-6 (5), 7-5 to even their matchups at 4-4. Petrova, who had to qualify after an injury-plagued 2013 dropped her singles ranking to 100, almost pulled off the win despite nine double faults.
Tsvetana Pironkova of Bulgaria defeated Roberta Vinci of Italy 6-3, 6-3 for the first time in four matches, while Annika Beck beat Mona Barthel in their all-German match 7-6 (5), 6-2 for the first time in three matches.
Taiwanese qualifier Hsieh Su-wei won for the first time against Italy's Flavia Pennetta 7-5, 6-3, and Czech qualifier Petra Cetkovska beat American Sloane Stephens 7-5, 6-1. Stephens, who'd beaten Cetkovska at the last two Wimbledons, rallied to level at 5-5, but could win only one more game as she lost her serve five times.
The field features seven of the top 10, led by Australian Open champ Li Na who, regardless of her result this week, will move to a career-best No. 2 ranking next week, above Victoria Azarenka, the two-time reigning Doha champ who was absent with a foot injury.