Rickie Lambert was absent for Nigel Adkins' side with a hip injury and the Saints badly missed the 14-goal striker's cutting edge as they failed to consistently test Rovers goalkeeper Carl Ikeme at the Keepmoat Stadium on Saturday.
Southampton's best chance fell to Morgan Schneiderlin, who was thwarted by on-loan Wolves man Ikeme when through on goal in the first half.
An end-to-end opening period gave way to a cagey second 45 minutes, but Sharp was on hand to provide the decisive moment from Marc-Antoine Fortune's 60th-minute cross.
West Ham's defeat to Burnley means Southampton's two-point advantage at the summit remains intact after 20 games.
James Coppinger replaced Giles Barnes in the only change to the Doncaster side that lost 3-2 at Millwall on Tuesday night, while Adkins handed recalls to Danny Fox and Steve de Ridder.
Rovers might have taken a second-minute lead when Herita Ilunga headed wide after the Saints defence gifted the on-loan West Ham defender a free header from Brian Stock's corner.
Former St Mary's midfielder Simon Gillett then drew an impressive save from Kelvin Davis with a stinging 20-yard drive as Doncaster made an enterprising start.
Sharp dragged wide from a Gillett cross in the 24th minute before Stock fired narrowly past the post from the edge of the area after full-back James O'Connor instigated a swift Rovers counter-attack.
Southampton should have been in front shortly after the half-hour. Schneiderlin sprung the Doncaster offside trap to collect Guly Do Prado's through-ball, but Ikeme was quickly off his line and diverted the ball behind.
From the resulting corner, one of eight won by Saints in the opening period, the hosts sprung up the other end on the counter-attack to win one of their own, and Ilunga saw his header from Stock's delivery cleared off the line by Jose Fonte.
Do Prado, who scored his eighth goal of the season in Southampton's midweek victory over Hull, hit a speculative lob in the 39th minute, forcing a scrambling Ikeme to tip over the bar.
That save preserved the deadlock at the interval and the high-octane nature of the first half was not replicated when the action resumed.
But the Keepmoat Stadium was sent into raptures with an hour gone when Fortune hared towards the right byline and cut back for Sharp to register his seventh goal of the season in clinical fashion.
Sharp netted from the penalty spot in midweek and after 74 minutes it looked as if he might get the chance to double his side's advantage when Coppinger went down under a heavy challenge from Fox in the area. However, the linesman's flag was already raised for offside.
In the final quarter of an hour, Southampton remained frustrated as a dogged Doncaster secured three vital points.