Derry midfielder Philip Lowry was sent-off as the Candstripes were beaten by Sligo in the basement battle.
Rovers led through Tim Clancy's header in on 19 minutes but Derry improved before the break with Mark Timlin and Cillian Morrison going close.
The visitors were edging affairs when Lowry was shown a straight red after an off-the-ball incident with Raffaele Cretaro in the 59th minute.
Sligo stay in the relegation play-off spot but are level on points with City.
The hosts seized control after a frenetic opening at the Showgrounds with Jason Hughes fizzing over and John Russell heading wide.
Clancy's downward header from a corner put Rovers in front and Derry suffered a further blow when Aaron McEneff was forced off injured, with Cillian Morrison his replacement after 29th minutes.
City finished the first half strongly, with Mark Timlin shooting over while Morrison shot straight at keeper Richard Brush before the striker headed wide.
The impressive Timlin rifled narrowly over on the restart but Derry's momentum was halted by Lowry's dismissal, City's second in two games after Conor McCormack's red card against Dundalk.
Morten Neilsen sent his free-kick just wide and Russell's effort flew over the bar but Sligo's failure to capitalise with the extra man gave Derry hope of snatching a late equaliser.
Timlin squandered the opportunity when he volleyed wide with a minute left while Gerard Doherty made an injury-time save to deny Russell.
Derry take a welcome break from league action on Friday night with a FAI Cup clash with Drogheda United at the Brandywell.