When Spurs did fashion a decent chance, Kranjcar hit his volley into the ground and wide.
Niko Kranjcar put Spurs ahead, tapping in after Stephen Ireland had blocked Peter Crouch's initial header.
Niko Kranjcar clipped in a second but the hosts barely got out of first gear.
Kranjcar, who had got the final touch after Lomana LuaLua's initial shot was saved, looked mystified.
BBC: Portsmouth and Arsenal found each other hard to break down
Sunderland were holding their own, though, until Phil Bardsley felled Nico Kranjcar and Defoe scored the penalty.
Kranjcar provided Pompey with the perfect start after only four minutes with his first goal for the club.
Portsmouth did manage to build some passages of possession, mainly through Diarra, Baros, and the impressive Niko Kranjcar.
Kranjcar then secured Pompey's win when he powered in a 25-yard free-kick from the right side of Birmingham's area.
Kranjcar drove in from the right and finished with aplomb to add the polish to an accomplished Spurs performance.
Kranjcar, though, feels the player has only himself to blame for his difficulties.
Bolton were denied a penalty after an apparent foul on Gary Cahill, before Kranjcar won it with a 25-yard strike.
Tottenham then suffered a blow when Bale, who required lengthy treatment in the first half, was replaced by Niko Kranjcar.
Benjani put in a dangerous cross early on, while Kranjcar went close with a shot from just outside the box.
Not surprisingly, Harry Redknapp made two changes at half-time, Jermain Defoe and Niko Kranjcar brought on for Assou-Ekotto and David Bentley.
Muntari had the first decent effort at goal, driving narrowly over with a 25-yard free-kick, while Herman Hreidarsson headed wide from a Kranjcar corner.
Jermain Defoe had a near-post volley saved, Robbie Keane headed over and Niko Kranjcar struck a volley wide as Spurs struggled to find a way back.
Midfielder Niko Kranjcar followed Lassana Diarra, Jermain Defoe, Glen Johnson and Peter Crouch out of Fratton Park after agreeing a switch to Tottenham on 1 September.
England went 2-0 down when Scott Carson, in for Paul Robinson, fumbled Nico Kranjcar's shot into the net and then Ivica Olic slipped in a second.
Kranjcar, the father of Tottenham midfielder Nico, has lifted his team to the top of Group G after three 1-0 victories against Wales, Bulgaria and Switzerland.
"I am sure it is very difficult for Rooney, but he got himself into this situation, " said Kranjcar, who took over as Montenegro coach in February.
However, the match was decided by Bardsley's foul on Kranjcar, the Croatian bamboozling the Sunderland full-back before tumbling over his leg and Defoe dispatched the penalty with aplomb.
Pedro Mendes and Sulley Muntari have left the club while Niko Kranjcar is sidelined following an ankle injury - leaving Redknapp without three of his FA Cup Final midfielders.
Portsmouth continued to dominate after the break, with Mendes shooting just over the top and Kranjcar coming closest of all when he narrowly failed to turn in Glen Johnson's cross.
And he has joined the trail set by Glen Johnson, Dimi Traore, Sean Davis, Peter Crouch, Sol Campbell, Sylvain Distin and now also Niko Kranjcar in leaving Pompey this summer.
Crouch replaced the enigmatic, and on this occasion ineffective, Roman Pavlyuchenko, and the England striker scored with his first touch when he rose to meet Kranjcar's looping cross from the left.
Lennon and Crouch took a short corner allowing the former to feed Kranjcar, who nipped the ball past a static Adebayor before slotting under Given for his second of the game.
Keane sent Niko Kranjcar away down the left channel, his shot was blocked but Jenas followed up with a fierce long-range effort, that deceived Jensen after a cruel deflection off Stephen Jordan.
Gudjohnsen's dummy allowed Croatia midfielder Kranjcar to put the Londoners four points clear of fifth-placed Liverpool , who will have played one more match after Sunday's trip to bitter North-West rivals United.
Spurs thought they had swiftly restored equality when Crouch bundled the ball into the net, but referee Alan Wiley adjudged that Niko Kranjcar had fouled James as he challenged for Bale's cross.
Niko Kranjcar tried his luck on the unpredictable surface with a speculative 25-yard effort and Aston Villa's Carson allowed the dipping drive to bounce in front of him and skid into the net.
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