Ivorian attacker Gervinho slid home the opener in the 17th minute after a defensive mix-up.
Destro doubled the lead with his eighth league goal of the season three minutes before the break as Rudi Garcia's side moved on to 64 points, six clear of third-placed Napoli who host Fiorentina on Sunday.
Roma are 11 points adrift of Juventus who are clear favourites to win at rock-bottom Catania on Sunday.
"I think I did my job just as the manager asked and what's important to me is always to be ready when I'm called upon."
Chievo stayed fifth from bottom, level on 24 points with Livorno who lost 3-1 at Torino after a stunning Ciro Immobile hat-trick.
Immobile's treble put him top of the league's scoring charts on 16 goals and should make Italy manager Cesare Prandelli sit up and take notice of the 24-year-old.
"Prandelli knows how much effort I put into everything I do. If he decides to call me up I'll give my all," said the Torino forward.
Chievo and Livorno are one point above the drop zone. Third from bottom Bologna take on Cagliari on Sunday.
A defensive howler let Gervinho in for Roma's opener.
Chievo defender Bostjan Cesar had lots of time to clear a hopeful punt but headed weakly back towards keeper Michael Agazzi, allowing the Ivorian to pounce.
Another bad back pass from Dario Dainelli gifted the ball to Destro and, instead of shooting, the Roma striker tried to round the keeper and could only crash a poor shot into the side netting.
The 23-year-old then grabbed his second goal in as many games as he expertly collected Taddei's incisive through ball and shot into the bottom corner.
Despite a better display from Chievo in the second half it was such a comfortable night for Roma that Garcia took off 37-year-old captain and talisman Francesco Totti, whose form has led to talk of a place at the World Cup in Brazil in June, with half an hour left.
The only sour note for the visitors was the late booking for central defender Mehdi Benatia who after picking up his eighth yellow card of the season will be suspended for next week's clash with Torino and red-hot striker Immobile.
"It looked easy because we played so well in the first half. I didn't like the second half as much but we didn't concede," said Garcia.
"I have players that always want to win. They don't take anything for granted."
Under-fire Dutch coach Clarence Seedorf takes mid-table AC Milan to Lazio on Sunday where the home fans will be carrying out the latest in a series of protests against president Claudio Lotito.
- Sports & Recreation
- Rudi Garcia
- Rodrigo Taddei
- Kevin Strootman