Sharapova, competing for the first time since retiring from her first-round match at Wimbledon, appeared to be on course for just a fourth match win since January when she went up a set and an early break on the 16th seed from Estonia.
England's record wicket-taker broke down after just four overs in the series opener at Edgbaston and did not bowl again as Australia romped to a 251-run victory.
Joe Root insisted England would avoid pressing the panic button after going 1-0 down in the Ashes with a crushing 251-run defeat in the first Test at Edgbaston.
Sebastian Vettel came home third ahead of team-mate Charles Leclerc, but both conceded that they could not generate the pace to compete with Hamilton's Mercedes or the Red Bull of second-placed Max Verstappen at the Hungaroring.