World number one Sharapova, who elected to come off court in the Wednesday night gloom when leading by a set and 3-1 against dangerous grasscourter Tsvetana Pironkova, went into meltdown for a while on the resumption in sticky lunchtime heat on Court One before prevailing 7-6 6-7 6-0.
Serena, the four-times champion who Sharapova beat to win her sole Wimbledon crown in 2004, was far more ruthless in a 6-1 6-4 defeat of Hungarian qualifier Melinda Czink.
The sixth seed, who has not added to her 13 grand slam titles since returning this time last year from a career-threatening foot injury and health problems, was razor sharp as she booked a third-round clash with China's Zheng Jie.
With sunshine and high temperatures replacing the frustrating drizzle of the day before which prompted the closure of the Centre Court roof, organisers worked through a small backlog of postponed and unfinished second round matches in the top half of both singles draws.
In the bottom half, Britain's Andy Murray was braced for a barrage of fast serving from Ivo Karlovic in their second round tie while twice former champion Rafael Nadal was the last match scheduled on Centre Court against Czech Lukas Rosol.
Women's champion Petra Kvitova faces Briton Elena Baltacha.
Sharapova had saved five set points against the 2010 semifinalist Pironkova on Wednesday before moving into a commanding position – only to pack her bags three games shy of victory.
That decision looked odd at the time and even more so as she made a ragged start on Thursday.
Pironkova, whose serve is a real weapon, immediately got back on level terms at 3-3 and when the second set reached a tiebreak she went 6-1 ahead.
Sharapova again saved a couple of set points before sending a forehand long and set up what could have been a nervy decider.
Pironkova double-faulted on a game point at the start of the third and that proved the spark for Sharapova to catch fire again and rattle off six successive games and set up a meeting with Taiwan's Hsieh Su-wei. Unlike Williams, though, she will not get a rest day and will be back on court on Friday.
"I started with no motor whatsoever and felt like I was [stuck] on pause," Sharapova, who was clearly not happy with her performance, particularly on serve, told reporters.
"But she is someone who comes out and fires. If she played on grass 365 days a year she would be in the top five."
While all eyes remain on the men's "big four" two of the new generation continued to impress on Thursday as they moved into the third round.
Kei Nishikori, the 19th seed, beat France's Florent Serra 6-3 7-5 6-2 to become the first Japanese male player to reach the third round of the Wimbledon singles since Shuzo Matsuoka 17 years ago.
Belgian David Goffin, who gave Roger Federer a big scare at the French Open this month, backed up his impressive first round win over Australian 20th seed Bernard Tomic with a four-sets victory over American Jesse Levine. – Reuters