Scotland international Kyle broke the deadlock on the hour and Whitley made up for the disappointment of missing out on the Black Cats' FA Cup semi-final tie against Millwall or Tranmere Rovers because of suspension with his first goal for the club in the 72nd minute.
West Ham had to overcome the early loss of Matthew Etherington, who scored a hat-trick in the midweek victory over Wimbledon. He was stretchered off in the 15th minute following a tackle by Whitley.
Sunderland, with games in hand are in a strong position to mount a swift return to the Premiership and the return to action of Matt Piper for a brief substitute appearance after missing most of the season through injury was a big bonus.
Chances were few and far between for both sides who had no trouble in finding the net in midweek in their respective matches with Whitley squandering Sunderland's best opportunity just before the break.
Bobby Zamora, Jobi McAnuff and Marlon Harewood threatened briefly but it was the home side who made the breakthrough on the hour.
Kyle won in the air and when Tommy Smith failed to apply the finishing touch, Kyle hooked the ball across Stephen Bywater and just inside the upright.
The Hammers' response was to throw on Brian Deane and attempt to cause aerial problems, but after Harewood had failed to take full advantage of a George McCartney slip, the home side struck again.
Bywater saved well from John Oster, but the ball broke from his grasp and the persistence of Whitley won the day as he poked home his first goal for the club.
Piper showed some neat touches after replacing Oster in the 79th minute, cutting in from the left to test Bywater before the visitors applied late pressure.
But their efforts were in vain as Sunderland, marshalled superbly at the back by Gary Breen and Phil Babb, stood firm to deny the Hammers any way back.
Man of the Match: Gary Breen – Gave a dominant display against one of his former club to see Sunderland through to a crucial victory.