When Rovers defender Dennis Souza received his second yellow card in the 58th minute, the stage was set for United to emerge victorious on Micky Adams' home bow at Bramall Lane.
The boyhood Blades supporter, 49, was last week handed a two-and-a-half year deal as successor to Gary Speed.
Yet Sharp, another lifelong United fan, who failed to sparkle during his own time at Bramall Lane, opened the scoring in the 66th minute and rifled home a second from the penalty spot eight minutes later to put Doncaster 2-0 up.
Substitute Daniel Bogdanovic's close-range volley offered United hope in the 86th minute and Kozluk's late volleyed equaliser averted a fourth straight defeat.
Source: PA
Source: PA