Top seed Williams surpassed rising French star Caroline Garcia 6-4 4-6 6-4, in what was a rhythmic affair at the WTA Premier event in Miami.
Five consecutive breaks of serve from 1-1 in the first set was snapped by a Williams hold, and the American went on to serve out the set.
Only one break point chance was seen in the first nine games of the second set but that did not stop Garcia from breaking Williams in the 10th game to level the match.
As soon as Garcia got the momentum, she handed it back, as Williams broke serve in the first game of the third set - and there would be no more breaks for the remainder as the world number one survived the scare.
Sharapova, the Russian fourth seed, got past Czech left-hander Lucie Safarova 6-4 6-7 (7-9) 6-2.
The four-time major winner had match points in the second set tie-break but could not convert, although Safarova's comeback was thwarted in the first game of the decider as Sharapova broke and never rescinded her advantage.
Safarova - the 26th seed - showed some resilience, though, saving a total of eight match points for the encounter before Sharapova finally won.
Ninth seed Sara Errani of Italy was sent packing from the hard-court tournament, with Russian 23rd seed Ekaterina Makarova posting a 6-3 2-6 6-4 triumph.
Serbian 12th seed Ana Ivanovic ended the winning run of Italy's Flavia Pennetta, who had claimed the WTA Premier title at Indian Wells.
Pennetta, the 20th seed, was beaten 6-4 6-3.
German fifth seed Angelique Kerber was a 6-0 6-2 winner over Bulgaria's Tsvetana Pironkova, while eighth-seeded Czech Petra Kvitova accounted for Croatia's Donna Vekic 6-3 6-4.
Belgium's Kirsten Flipkens received a walkover after Sabine Lisicki of Germany withdrew, while American Coco Vandeweghe ousted 16th seed Sam Stosur of Australia 5-7 7-5 7-5.
Williams, Sharapova pull through at Sony Open
