The midfielder scored the only goal of the game in the first half but the visitors wasted several good chances to walk away with at least a point.
Miralem Pjanic was Roma's hero as his 25th minute strike secured a 1-0 win over Napoli, but the home side had Morgan De Sanctis to thank for an inspired second-half display.
The midfielder stroked home the only goal of the game from Alessandro Florenzi's cutback, but the second half belonged to the visitors, with Dries Mertens and Manolo Gabbiadini both denied by the Giallorossi keeper.
Victory leaves Roma within touching distance of qualifying for next season's Champions League as it sits four points clear of third-place Sampdoria and 11 adrift of leader Juventus.
The opening 20 minutes passed without incident, with a 20-yard free kick from Napoli’s Faouzi Ghoulam the only effort of note, which curled straight into the arms of Roma goalkeeper De Sanctis.
But with 25 minutes gone the home side took the lead. Juan Iturbe drew four Napoli players toward him on the edge of the box and fed Florenzi down the right, who cut the ball back for Pjanic to slide home.
It was a rare moment of quality in a first half bereft of attacking inspiration, though Napoli did engineer a great chance to level before the break.
A wonderful through ball from Gonzalo Higuain played in Jose Callejon behind the Roma back four, but he turned inside and laid the ball to De Guzman, whose shot was blocked by Manolas, when he should have gone for goal himself.
Up the other end, Pjanic played Ljajic through down the left but his cross-shot couldn’t find a Roma shirt, before Higuain’s curler flew narrowly over from a tight angle as the first half drew to a close.
After the break, Mertens came close to making it 2-1 in the 52nd minute. The winger sped past Davide Astori on his way into the box but his shot with the outside of his right boot lacked the power to trouble De Sanctis.
Napoli continued to carry the greater threat and a surging run and cross from De Guzman found substitute Gabbiadini, whose first-time volley was brilliantly touched over the crossbar by the keeper.
The forward was in the thick of the action just moments later. Mertens danced his way inside the box yet again before feeding his teammate, but his left foot shot was straight at De Sanctis, who smothered.
Roma had offered nothing in attack but could and should have made it 2-0 late. Victor Ibarbo's through ball set Iturbe free but after rounding Mariano Andujar he fired the ball into the side netting.
The hosts held on to secure their first home win of 2015 and take a big step toward securing the second Champions League place in Serie A.