Ryder Cup team-mates Harrington and Westwood each shot a three-under-par 69 at Redstone Golf Club in Humble, Texas, to lie two shots behind first round co-leaders Kevin Stadler of the United States and Australian Cameron Percy.
England's Casey, who landed his first US PGA Tour victory in the event 12 months ago, had earlier suffered a blow to his Masters build-up when he was unable to defend his title.
The world number six, who was due to partner Phil Mickelson in the opening two rounds, tweaked a muscle in his back near his left shoulder and withdrew just before his 8am tee-off time.
Casey said it was not related at all to the torn chest muscle which kept him out of action late last season and hoped it was a just a "sleeping wrong" problem which would quickly respond to treatment.
In his absence, Ireland's Harrington was the pick of the early European starters, the three-time major winner continuing his good recent form with a five-birdie, two-bogey opening round.
He was joined on three under by Westwood, who shot a bogey-free 69 and like all the afternoon starters had to deal with far more windy conditions than the earlier wave.
Americans Anthony Kim, Vaughn Taylor, Kevin Sutherland and James Driscoll were in a tie for second on four under with Harrington, Laird and Westwood in an eight-man group that also included Mickelson and Australia's Adam Scott.
Scotland's Martin Laird was a further shot behind on two under having finished bogey, birdie, bogey playing the front nine last and also shooting a 70 were England's Justin Rose and South African Ernie Els, who is bidding for a third straight win following successes at the CA Championship and Bay Hill Invitational.
Dubliner Harrington had gone on a run of birdies at the 14th, 15th and 16th but then his second bogey of the round came at Redstone's tricky 488-yard, par-four 18th as he over-compensated for the lake down the left of the fairway by finding a right-sided bunker.
Masters champion Angel Cabrera, Germany's Martin Kaymer, Sweden's Carl Petterson and Denmark's Soren Kjeldsen all carded 71s and Englishman Chris Wood shot a 72.
England's Luke Donald and Simon Dyson, and Sweden's Fredrik Jacobson finished the day with 73s, one over par.
Northern Ireland's Rory McIlory had a card showing three birdies, three bogeys and double bogey as he posted a two-over 74 alongside Norway's Henrik Bjornstad, while Sweden's Daniel Chopra hit a 75 and England's Brian Davis signed for a 76.
Greg Owen withdrew due to illness following an opening 79, while Vijay Singh had been seven over after nine holes when the Fijian also withdrew from the tournament, citing a bad back.
