Morrison slotted home just after the break, before Ifill scored with his first touch after coming on as a late sub.
Coventry had been given an opportunity to get back to 1-1 before that, but Irish midfielder Michael Doyle had a 60th minute penalty saved by Julian Speroni.
Crystal Palace had the best of the early exchanges and young forward Sean Scannell looked particularly dangerous.
The 17-year-old cut past Ben Turner in the Coventry defence in the second minute but his shot from a tight angle was saved by recalled keeper Andy Marshall.
James Scowcroft followed up but his effort was stopped by a combination of Marshall and a City defender.
Scannell went through again after five minutes as the home team's offside trap failed badly and Marshall was forced to save again as he came out to the edge of his area.
Coventry full-back David McNamee limped off after just seven minutes with a hamstring injury to be replaced by Julian Gray.
Iain Dowie's side finally put together a decent move after nine minutes which involved Doyle, Stephen Hughes and Jay Tabb, before Leon Best's low shot was well saved by Speroni.
Marshall set up a chance for Coventry on the half-hour mark with a superb kick to Michael Mifsud. The little striker pulled clear of the Palace defence and crossed for Best who volleyed wide.
From the resulting corner, Hughes was given a free header at the near post but he tried to use his left foot and the chance was lost.
Ben Watson tried his look from distance in the 37th minute but again Marshall was equal to it.
Marshall made another important stop as Morrison looked clean through but the Coventry goalkeeper made himself big and saved well.
But Morrison did open the scoring just after half-time when a free-kick from Watson was allowed to roll through to him and he had all the time in the world to plant his shot into the Coventry net.
Gray did well to cut past two Palace defenders in the 58th minute and crossed for Best who headed wide.
The home team were handed a golden chance to draw level on the hour mark when the referee's assistant spotted Clint Hill tugging at Best in the box.
Doyle stepped up but Speroni saved the penalty low down to his left.
Mifsud broke clear two minutes later but his shot was again repelled by the Palace keeper.
Coventry had improved in the second half and Hughes tried his luck from distance after 68 minutes only for Speroni to save again.
Palace doubled their lead late on when substitute Ifill took advantage of more slack defending to fire past Marshall in the 88th minute.