Inter Milan can re-establish their two-point lead with victory at Roma's city rivals Lazio on Sunday but Claudio Ranieri's side made sure the pressure will be fully on the champions with just two games left after this weekend.
"A top performance on a difficult ground against a team with no pressure. It's a great victory," Roma midfielder Daniele De Rossi told Sky TV.
Valeri Bojinov fired just wide for the mid-table hosts on five minutes before Roma, workmanlike on Labour Day, went straight up the other end and scored.
De Rossi pinged a pass forward and captain Totti timed his run to perfection, chested the ball down and lobbed goalkeeper Antonio Mirante from 18 metres.
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The striker, who also hit the post, later sent in a delightful cross which Rodrigo Taddei nodded in for the second goal on 75 minutes.
Davide Lanzafame's superb header set up a nervous finish during which Parma's Luis Jimenez was sent off.
Totti's display and his 12th league goal of an injury-hit season offered food for thought for Italy coach Marcello Lippi as he considers whether the 33-year-old should come out of international retirement and play at the World Cup in June.
The Roma player though will be missing from Lippi's World Cup training camp this week along with team-mate Luca Toni, who came on at half time, because the club are playing Inter in the Italian Cup final on Wednesday.
Roma surrendered the title initiative in the two-horse race when they lost 2-1 at home to Sampdoria last weekend, their first defeat in 25 Serie A games.
Third-placed AC Milan, whose coach Leonardo has hinted he will soon leave because of a difficult relationship with owner Silvio Berlusconi, beat mid-table Fiorentina 1-0 thanks to a 77th-minute penalty from the inconsistent Ronaldinho.
Their first victory in four games, which featured much huffing and puffing before Marco Borriello was felled in the box, means the Rossoneri moved seven points clear of Sampdoria in the race for the final automatic Champions League spot.
Milan had skipper Massimo Ambrosini sent off late on but Fiorentina barely threatened, to the annoyance of coach Cesare Prandelli who has committed to the club but is still an outside bet to be Italy or Juventus boss next term.
