Rovers played out the last four minutes a man down after Paul Heffernan was sent off for head-butting Charlie Mulgrew.
Doncaster shaded the opening exchanges and saw a driven 35-yard effort from James Coppinger fizz inches wide of Darryl Flahavan's right-hand post.
Mark Gower got Southend's first effort on target with a 25-yard effort that veteran Doncaster keeper Neil Sullivan smothered at the near post.
Doncaster went close when skipper Brian Stock's free-kick was headed just wide of the far post by Matt Mills.
Southend then tested Sullivan with a header from skipper Adam Barrett, before Mulgrew's cross-cum-shot from 40 yards was caught by the keeper.
Lee Barnard then saw his goalbound shot from 12 yards deflect out for a corner, before Flahavan made a reflex save to deny Paul Green a deflected goal.
The Shrimpers had the last say of the half with Simon Francis' effort from a Gower cross being parried by Sullivan.
Flahavan kept the Blues in the match minutes later when he palmed Stock's free-kick from the edge of the box out for a corner.
Rovers upped the pressure with a disappointed Heffernan firing wide from Lewis Guy's pass.
The best chance of the night fell to Rovers striker Jason Price, who found himself one-on-one with Flahavan but saw the keeper palm away his effort from 12 yards.
Southend thought they had got a goal advantage to take to the Keepmoat Stadium, but Barrett's goalbound header from a Nicky Bailey cross was deflected to safety.