Vladimir Petkovic's men got the better of the Giallorossi in a thrilling match that included five goals, including one from the halfway line, and a red card for both sides
Goals from Antonio Candreva, Miroslav Klose and Stefano Mauri were enough for the home team at Stadio Olimpico despite efforts from Erik Lamela and Miralem Pjanic narrowing the deficit.
Daniele De Rossi's straight red card on the stroke of half-time didn't aid Roma's cause as they suffered defeat for the third time in their last four matches, whilst Mauri was sent off late on for a second bookable offence.
After a floodlight failure halted the match for around five minutes, Roma took an early lead as Lamela headed in Franceso Totti's corner for his seventh goal in his last six matches for Zdenek Zeman's side.
The Biancocelesti were slightly aggrieved that they were not awarded a free kick in the build-up to the goal, but they almost pulled level almost immediately as Hernanes tested Mauro Goicoechea from distance.
Totti was at the heart of everything Roma were producing, and he forced Federico Marchetti into a smart save as his low shot from the corner of the box was well parried by the goalkeeper.
Klose was back from suspension for the home team, and he posed his first threat as his header was turned away well by Goicoechea, though the referee had already blown for a foul earlier in the move.
Persistent heavy rain was making the playing conditions increasingly difficult and meant the number of chances were much fewer, though Abdoulay Konko went close as his flicked header from Hernanes' free kick went just over the bar.
Lazio were then gifted an equaliser as Candreva's powerful free kick was straight at Goicoechea, but the young Uruguayan could only parry the ball into his own net, with the slippery conditions probably having played a part.
Vladimir Petkovic's side had their tails up, and they almost hit Roma on the counterattack as Candreva broke away down the right before finding Klose on the edge of the area, but the Germany international could only fire over.
With three minutes remaining of the first half Lazio did take the lead as Klose turned in Hernanes' low cross-cum-shot for his seventh Serie A strike of the campaign.
Roma's first half went from bad to worse in stoppage time as De Rossi received his marching orders for a slap on Mauri when awaiting a free kick on the edge of the area.
It took Lazio just 90 seconds of the second period to extend their lead as Ivan Piris' weak defensive header fell at the feet of Mauri on the edge of the area and he made no mistake in slotting it past Goicoechea.
Petkovic's team were relentless in their attacking and Goicoechea had to pull of an acrobatic save as Hernanes' shot was heavily deflected to leave the goalkeeper slightly wrongfooted.
Roma pushed for an opportunity to get back into the game, but they almost fell further beind when Candreva fired a low shot across goal that Goicoechea held onto well.
The Giallorossi should have pulled one back when Pablo Osvaldo found himself free in the box from Totti's corner but he couldn't control his header and saw the ball disappear over the bar.
Hernanes continued to pose a threat from midfield and he almost got himself on the scoresheet but his low curling effort from 20 yards was turned around the post by Goicoechea at full stretch.
Zeman's team continued to press and substitute Marquinho threatened with a shot from just outside the box that went narrowly over Marchetti's crossbar.
Mauri received his second yellow card after he was adjudged to have handled on the halfway line, though replays suggested it may have hit his shoulder.
Roma capitalised on the decision as Pjanic scored directly from the free kick as Marchetti was caught off his line and couldn't keep out the speculative effort from all of 50 yards.
The 2001 Serie A winners pushed for a late equaliser and Osvaldo should have provided it as his reached Michael Bradley's searching pass but could only volley wide when clean through on goal and Lazio survived to claim a victory that ensures that they remain fifth in the standings, one place but now five points above their city rivals.