Doncaster failed to win at home for the first time this season in a hard fought top four battle.
Both teams had a man sent off in the eighth minute but despite the open nature of the game neither side could find an end product to their attacking play.
Southport skipper Steve Soley was shown the red card for a two-footed challenge on Jamie Paterson who was also dismissed for retaliation.
The visitors had started promisingly before the incident and Steve Pickford had a curling effort saved following a corner four minutes later before Rovers took control.
Doncaster applied tremendous pressure but were unable to find the finishing touch after four successive victories at home.
Paul Green and Andy Watson were just unable to connect with a header across the face of goal from Paul Barnes in the 13th minute.
Then Robert Gill produced a brilliant piece of skill to bring the ball under control and whip in a 20-yard shot which was superbly saved by Steve Dickinson.
Dean Howell had an angled left-foot shot cleared off the line by Tim Ryan when Southport pushed forward on the counter in the 23rd minute.
Green should have give Doncaster the lead in the 36th minute but mis-kicked in front of goal with Dickinson stranded.
Play was more even after the interval but Doncaster were unlucky not to be awarded a 53rd penalty when Watson was brought down by Howell.
Both sides had chances to win the game in stoppage time with Steve Jones having a fierce shot brilliantly saved by Andy Warrington, before Watson fired straight at Dickinson from point-blank range