Croatian international Kranjcar scored only his second goal since a summer arrival from Hadjuk Split to add to Benjani Mwaruwari's opener to kill off a Liverpool side who rested a number of their stars.
Sami Hyypia pulled one back for Rafael Benitez's side who had one eye on Tuesday night's crunch Champions League semi-final against Chelsea.
The game sprung to life after a lacklustre first 20 minutes when Gary O'Neil was put through by Benjani and as he tried to curl his effort inside Jerzy Dudek's far post, the Polish international produced a wonderful fingertip save to deny him.
Pompey were denied of the services of sharp-shooting midfielder Matthew Taylor when the England candidate limped off after 21 minutes with an ankle injury. That disappointment was soon a forgotten memory when Benjani caught Gabriel Paletta napping after a long ball from goalkeeper David James.
The much maligned Benjani took one touch to lift the ball over Dudek before heading into an empty net.
Pompey soon doubled their lead with a goal of real class. Lauren's inch-perfect, first-time crossfield ball was controlled by Kranjcar on his chest.
The long-haired midfielder then progressed towards Dudek before finishing with the deftest of touches with the outside of his right foot.
Liverpool were shell-shocked and were reduced to long-range speculative efforts from debutant Emiliano Insua and Xabi Alonso, neither of which troubled James.
It was one of these long-distance efforts though that nearly clawed them back into the game when Boudewijn Zenden let fly from 35 yards, but the ball cannoned back off the crossbar.
Liverpool came out in the second half a different team, clearly embarrassed at their first 45 minutes and dragged themselves kicking and screaming into the game when Hyypia powered past Linvoy Primus to head home Robbie Fowler's corner.
Fowler then produced a classy attacking display in the second period, setting up chances for strike partner Craig Bellamy and a late attempt at goal for himself, but on each occasion he was denied by the defiant Pompey backline.