Despite making five changes from the team which beat West Ham last Monday in the Premier League, Harry Redknapp's side never looked in danger of being the victim of a major cup upset at White Hart Lane.
Kranjcar produced a man-of-the-match display with two goals, while Jermain Defoe and Robbie Keane completed the rout as Tottenham kept alive their hopes of winning the competition for the first time since 1991.
The home side should have broken the deadlock after just nine minutes and Defoe will be still be wondering how he missed one of the easiest chances of his career.
Gareth Bale raced away down the left and crossed in for Luka Modric whose shot deflected into the path of the England striker, who was totally unmarked but, with the goal at his mercy, he somehow managed to strike the ball against the crossbar from just three yards out.
Tottenham had another golden chance to break the deadlock just seconds later when Keane broke free into the box but fired his shot straight against the body of Joe Lewis.
Redknapp's side were denied by the woodwork once again on 26 minutes.
Defoe flicked a superb back-heel into the path of Kranjcar inside the box. The Croatian midfielder saw his shot beat Joe Lewis in the Peterborough but the ball cannoned back off the bar.
Tottenham finally got their just rewards when Kranjcar opened the scoring on 35 minutes.
Modric played a fantastic cross-field ball into the path of Kranjcar and he fired an unstoppable shot past Lewis into the corner of the net.
Who said that Harry Redknapp cannot play the Croatian pair in the same team and they could be crucial for the north London club over the next few weeks while Aaron Lennon recovers from his groin injury.
Bale could have added a second on 38 minutes when his dipping shot from the edge of the box produced a fine save from Lewis diving away to his left.
Lewis came to Peterborough's rescue once again just 60 seconds later when he made another terrific save to deny Tom Huddlestone's fierce drive from the edge of the box.
Kranjcar added his second of the game on 57 minutes. Keane fed the ball into Bale, who cut it back for the Croatian midfielder and he fired the ball past Lewis.
Peterborough refused to lie down and almost got themselves back into the game on 65 minutes.
Craig Mackail-Smith struck a powerful shot from the edge of the box which looked destined for the top corner, but Heurelho Gomes produced the save of the match when he superbly tipped the ball over the bar.
Tottenham put the game beyond the Championship side on 70 minutes.
Bale was involved in the heart of the action once again when he raced to the byline and crossed in for Defoe, who slid the ball past Lewis.
Keane completed the rout when he netted from the penalty spot in injury time after Chris Whelpdale brought down Danny Rose inside the box.