David Connolly scored twice in five minutes as Southampton reached the FA Cup second round with a narrow win.
The striker converted Adam Lallana's 63rd-minute cross from close range and then slotted a second soon after.
Michail Antonio made it three after a clinical counter attack but Rovers pulled one back through Darryl Duffy's fine close-range effort.
Jeff Hughes then converted a late penalty after a foul on Jo Kuffour but Rovers could not complete the recovery.
Southampton manager Alan Pardew told BBC Radio Solent:
"We're not the full ticket yet as a team because obviously we should have won that game 3-0 once we got the goals.
"I thought we didn't play particularly well in the first half but with the quality we've got in the team we got the three goals.
"We want a run at it, we've started OK and now we go to the second round."
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