The Bluebirds showed one change with Aaron Ramsey coming in for the injured Joe Ledley.
Although Wolves were without a number of cup-tied players they were still no place for Wales international striker Freddy Eastwood, who was on the visitors' bench.
Within two minutes of the opening whistle City went ahead when Ramsey sent Whittingham racing down the middle. As Wayne Hennessey came out to block, the former Villa midfielder slid the ball into the empty net.
City went further ahead in the tenth minute with a superb strike by Hasselbaink. He started the move by swinging a pass out left to Paul Parry who made ground before flashing a low cross into the danger area.
The ball ran to Hasselbaink who twisted one way before turning and whipping his shot into the top corner of the net.
Stephen McPhail earned himself a yellow card in the 32nd minute for needlessly kicking the ball away after conceding a free-kick.
Mick McCarthy's side were in such disarray that Eastwood was brought on in the 40th minute and immediately had Peter Enckelman diving low to save at the near post.
Parry's pace up front was giving the Wolves rearguard all sorts of problems and Hennessey was forced to race out of goal early in the second half as the visitors' defence fell wide open.
Wolves introduced two substitutes and pushed three men up front which pushed the Bluebirds back on defence for the first time during the game, but Glenn Loovens and Roger Johnson dealt with any danger and McCarthy's men were left to shoot from distance.
The busy Eastwood sent a snapshot just wide of the post in the 80th minutes, but it was a rare scare for the Bluebirds, who now had Steven Thompson battling up front in place of Hasselbaink.
City even brought on Trevor Sinclair and Darcy Blake in the final minute as they ran the clock down for an comfortable victory.