Boro came into the game on the back of six successive away wins and made life difficult for Darren Ferguson’s men.
But Doncaster stuck to the task at hand and finally got the breakthrough in the 85th minute when Tommy Rowe’s shot was deflected in off Fraser Franks.
“I thought we were in complete control of the game and it was a thoroughly deserved win against a stubborn team,” said Ferguson.
“We believed we would get the winner and we just kept on doing what we wanted to do.
“At times the tempo wasn’t what I wanted but full marks to the players for their concentration and determination.
“We had to be patient and also concentrate on not getting caught on the counter.”
John Marquis saw a header saved by Jamie Jones and Rovers loan signing Conor Grant curled a free-kick just wide.
The second half followed a similar pattern but it looked like being a frustrating afternoon when Harry Middleton hit the cross bar and Grant saw a shot deflected wide. Rovers’ persistence paid off though when the unfortunate Franks diverted Rowe’s shot into the bottom corner.
Doncaster Rovers: Marosi, Blair, Mason, Baudry, Butler, Rowe, Houghton, Grant, Middleton (Williams 67), Coppinger (Keegan 90), Marquis. Unused substitutes: Jones, Wright, Beestin, Alcock, May.
Stevenage: Jones, Henry, King, Franks, Ntlhe, Pett, Kennedy (McAnuff 73), Gorman, Tonge, Walker (Lee 63), Godden (Liburd 81). Unused substitutes: Schumacher, Day, Cowans, Johnson.
Referee: M Brown (East Yorkshire).