Chelsea cutting edge too sharp for Canaries
Wright-Phillips opened the scoring on 38 minutes as he fired home from the edge of the area, and Drogba scored his 26th goal of the season at the start of the second half.
Michael Essien scored a third in stoppage time before Andriy Shevchenko rounded off the victory in the final seconds.
The win means Jose Mourinho's side are still fighting for silverware on four fronts, with success in the Premiership, League Cup and Champions League still in sight.
Heading into this game, Chelsea were on a run of five successive victories without conceding a single goal.
Club owner Roman Abramovich was back in the stands after a five week absence, but his favorite player, the Ukrainian forward Shevchenko, started the game as a substitute.
Essien also began the game on the bench, as Arjen Robben, Mikel Jon Obi, Wright-Phillips, Khalid Boulahrouz and Geremi were restored to the starting line-up.
Championship side Norwich knew their best hopes of producing an upset in this fixture depended on the form of Dion Dublin and Darren Huckerby, and both players started, while Simon Lappin was also recalled to the midfield.
It took eight minutes for Chelsea to test their visitors, and it was Frank Lampard who fired in a free kick from 25 yards which David Marshall, the Norwich goalkeeper, pushed to safety.
It proved to be Marshall's last input to the tie, as two minutes later he twisted his ankle and was replaced by back-up stopper Paul Gallagher.
On 17 minutes Norwich almost edged in front. Dickson Etuhu poked a left footed shot on to the inside of the Chelsea post, but as Lee Croft attempted to stroke the follow up shot into the far corner, Boulahrouz sprinted back to make a vital interception.
Then, on 26 minutes, only a last ditch header from John Terry denied Huckerby a certain goal.
The opportunities were a sharp warning for Chelsea, and almost immediately Gallagher made a diving save to deny a drive from Robben.
Lampard tested the Norwich keeper next, and on 38 minutes the Premiership champions finally found a way through. Another Lampard shot deflected into the path of Wright-Phillips, and the winger hit a shot from the edge of the penalty area which skimmed off defender Andy Hughes and beyond Gallagher.
Ghanaian international Essien was forced to return to his unfamiliar role of centre back just before half-time, after a shoulder injury forced Boulahrouz out of action.
Within six minutes of the second half, any hopes Norwich had of taking anything from this encounter vanished. Chris Brown failed to control a Lampard corner kick, and the ball fell to Drogba in the six yard box for the Ivory Coast international to slot home.
Shevchenko was brought on with 20 minutes remaining, to give talisman Lampard a rest ahead of a tough week which includes a Champions League fixture at FC Porto, and the League Cup final against Arsenal next weekend.
Forward Brown missed a chance to give Norwich a lifeline soon after, and then Croft had a lob tipped onto the crossbar by Petr Cech, before Dublin had a header saved.
Essien tapped in a third goal in injury time after good work from Shevchenko and the striker put a smile on Abramovich's face by heading home a Salomon Kalou cross in the dying seconds.