The hosts had endured a poor run of form in recent weeks, losing four of their past six games, but Sunday's Championship win moves the sixth-placed Bluebirds five points clear of Sheffield United, who visit the Welsh capital on Wednesday, with a game in hand.
An excellent strike from McCormack, meeting a Whittingham corner, had given Cardiff an early lead.
From that point, the relegation-threatened Hornets were the better side but they were punished for a failure to take their chances when Whittingham headed in his 21st goal of the season after 63 minutes.
Burke added a third after a fine run in the 78th minute before Heidar Helguson got a late consolation for Watford.
The Bluebirds were without defender Kevin McNaughton, who was ruled out with a thigh injury, while Anthony Gerrard was also an absentee with a calf strain. Striker Michael Chopra returned from a two-match suspension on the bench with Gabor Gyepes fit to start at the back.
Watford were without centre-back Jay DeMerit and midfielder Henri Lansbury after they suffered back and hip injuries respectively. Lee Hodson came in for DeMerit with Adrian Mariappa moving into the centre of defence.
The home side have relied heavily on Whittingham's goals from midfield this season, but he turned creator to give Dave Jones' side the perfect start in the seventh minute.
His pinpoint corner to the far edge of the penalty area found McCormack and the striker showed excellent technique to meet the ball on the half-volley and flash a low strike beyond Scott Loach for his fourth goal of the season.
Watford had made a timid start and the goal seemed to stun them into action with Will Hoskins seeing his spectacular overhead effort go just over the crossbar from a Don Cowie corner.
The visitors' best chance of an equaliser looked to be from their set-piece with Helguson seeing his 24th-minute header deflected wide before Martin Taylor hit the post from the next corner, with Cardiff keeper David Marshall relieved to recover the loose ball.
Watford continued to pile on the pressure, much to the frustration of the home faithful and, after yet another corner, captain John Eustace looped a header of the crossbar.
Tom Cleverley then freed Hoskins down the right and it took a superb clearance from Paul Quinn to deny Helguson a simple tap-in when the ball was eventually fired across the box.
Jones brought Tony Capaldi on for Mark Kennedy at the interval to give the former Plymouth man his 200th career league appearance.
But the change made little difference to the pattern of the game with Hoskins continuing to prove a real handful for Gyepes and Darcy Blake in the Cardiff defence.
But Whittingham eased Cardiff's nerves as the Bluebirds grabbed their second goal in the 63rd minute.
Burke, who had been making little impact on the right flank, produced a high cross to the far post and Whittingham showed his strength to head the ball past a flat-footed Loach.
And it almost became 3-0 as Loach denied City skipper Jay Bothroyd by keeping out his header with an acrobatic save.
But Loach was beaten moments later when Burke embarked on a mazy run from the halfway line and, after briefly losing control, fired a low shot into the net.
Watford then got a deserved consolation late on as Helguson fired a fine shot beyond Marshall in injury time.