The visitors, who started the game inside the relegation zone, saw their hopes of climbing out of the bottom three dashed following Felipe's sending-off for a rash challenge on Edin Dzeko in the ninth minute.
Roma capitalised, taking the lead eight minutes later after Dzeko latched on to Stephan El Shaarawy's through-ball to score from six yards out.
Eight minutes after the break, Roma looked to have put the game beyond the reach of SPAL when Aleksandar Kolaraov was allowed plenty of space to cross for Lorenzo Pellegrini, whose bullet header proved too much for Gomis.
SPAL were given the chance to pull a goal back from a penalty almost immediately when Kostas Manolas scythed down Luca Mora.
However, Roma were able to keep the Biancazzurri at bay to move to within four points of leaders Napoli for the time being.body check tags ::