The Croatia international, whose stunning goal saw off Bolton last weekend, blasted home a 57th-minute volley to claim all three points as Spurs came from behind to win on Wearside.
A crowd of 40,986 saw the Black Cats take an 11th-minute lead when record signing Asamoah Gyan claimed his 10th goal of the season.
But the visitors levelled a minute before the break through Michael Dawson's header as they recovered from a poor start, and Kranjcar completed the job as they turned in a much better second-half display.
The win, which improved Tottenham's run to just one defeat in 15 league outings, lifted them above Chelsea, who do not play until Monday evening.
It also denied Sunderland the chance to reclaim sixth spot from Liverpool, who had drawn with Wigan earlier in the day.
The defeat was a third in succession for Steve Bruce's men, which they have not suffered previously in the league during his reign.
Tottenham arrived on Wearside with one eye on Tuesday's Champions League trip to AC Milan, and started as if they had as Sunderland took control.
The home side did not need long to get their noses in front, as Gyan turned expertly on Kieran Richardson's driven cross and smashed a right-footed shot past Heurelho Gomes.
That was just the platform the home side needed after successive league defeats by Chelsea and Stoke, and they looked capable of adding to their tally as Sulley Muntari protected the back four to allow Richardson, Stephane Sessegnon, Steed Malbranque and Jordan Henderson to provide the support to lone striker Gyan.
Benin international Sessegnon warmed Gomes' hands with a 14th-minute strike from long distance, and with Spurs misfiring alarmingly, there seemed little prospect of Sunderland surrendering their advantage.
Without the injured Rafael van der Vaart, Gareth Bale and Aaron Lennon, the latter who was named only among the substitutes, the visitors lacked real penetration.
And with the exception of the lively Kranjcar, Tottenham resorted to lumping a series of high balls in the general direction of Roman Pavlyuchenko, to little effect.
Kranjcar fired into the sidenetting from a 22nd-minute half-chance, and manager Harry Redknapp was rapidly losing patience on the sideline.
Spurs belatedly established a momentum late in the half and might have been level had the again impressive John Mensah not got to Benoit Assou-Ekotto's cross marginally in front of Jermain Defoe.
But they did equalise from the resulting corner when Dawson met Steven Pienaar's cross with a firm downward header, and with central defensive partner William Gallas partially blocking his view, goalkeeper Craig Gordon let the ball go between his legs.
The second half began with a flurry of activity as both sides created chances.
Full-back Phil Bardsley managed to clear Gallas' close-range effort off the line, and Gomes had to save from Malbranque and Sessegnon in quick succession at the other end.
But the third goal duly arrived, and when it did, it gave Spurs the lead for the first time.
Mensah got up well to head out Sandro's right-wing cross, but the Ghana international could only clear the ball as far as Kranjcar, who thumped a sweet volley into the bottom left corner.
Sandro got in a last-ditch block to deny Sessegnon a 59th-minute equaliser after Muntari had picked him out with a deep free-kick, but Pienaar fired just over from distance at the other end seconds later.
Muntari whistled a long-range effort just wide with 20 minutes remaining and Pavlyuchenko wasted good work by Jermaine Jenas by shooting weakly at Gordon two minutes later.
Richardson clipped the top of the crossbar with a deflected 79th-minute shot as the home side threw everything they had at Spurs.
Substitute Boudewijn Zenden drilled a late free-kick into the defensive wall as their cause became increasingly desperate, and Redknapp moved to shore up his midfield three minutes from time when he withdrew striker Defoe and sent on Wilson Palacios.
In the event, the Londoners saw out the game in relative comfort to send them on their way to Italy with a hard-fought win behind them.