Foxes goalkeeper Chris Weale was caught out by the set-piece specialist in the 78th minute as Whittingham whipped a left-footed effort inside the near post from out on the right-hand side.
Bluebirds boss Dave Jones will feel it was a deserved victory at the Walkers Stadium after watching his side create the most chances ahead of Wednesday night's second leg in Wales.
Leicester created little until the closing stages. Their best opportunity fell to substitute Matty Fryatt but keeper David Marshall stood up to block his shot when one-on-one with the striker.
Marshall then produced a superb reaction save deep into injury time to claw away Alex Bruce's header to edge Cardiff closer to a return to the top flight for the first time in 50 years.
Leicester made five changes. Weale returned in goal and Bruno Berner was recalled at left-back. Joint-leading scorer Martyn Waghorn came back into the side along with midfielders Andy King and Lloyd Dyer.
Michael Morrison failed to sufficiently recover from an ankle knock so Bruce kept his place alongside Jack Hobbs in the centre of defence, with Morrison on the bench.
Just like against Derby a week ago, Cardiff made nine changes. Mark Hudson and Chris Burke were the only survivors from Pride Park.
Joe Ledley, Whittingham, Jay Bothroyd and Michael Chopra were among the key players to return.
Cardiff created three chances dur the first half.
The first came after 10 minutes. Bothroyd brought down a long clearance from Marshall midway inside the Leicester half before turning and advancing towards goal.
His left-footed shot from the edge of the area rolled just wide of the post with Weale beaten.
It was from another surging run from Bothroyd midway through the first half that Cardiff went close again.
Bothroyd released his strike partner Chopra down the right side of the area but his shot across goal went wide of the far post when he really should have at least worked Weale.
Five minutes before the break, Ledley put Burke clear down the right-hand side. Chopra got across his marker at the near post but could only flick Burke's low cross against the woodwork from close range.
Cardiff carried their goal threat in to the second half and Bothroyd powered a header over the crossbar from Kevin McNaughton's cross.
It was not until the 53rd minute that Leicester produced their first noteworthy effort on goal as Richie Wellens' driven, low shot from 25 yards flew narrowly wide.
Whittingham put Cardiff ahead before Fryatt went clear in the 83rd minute.
McNaughton got back to make a challenge but the ball broke to Fryatt again only for Marshall to make the save.
Paul Gallacher curled a shot wide as Leicester searched for an equaliser.
It looked like they had got it at the death but Marshall's heroics to thwart Bruce preserved Cardiff's lead.