With the tournament still running behind schedule following extensive rain and wind delays on Thursday, Casey had played 36 holes on Friday but had to wait until 5.20pm local time at the Redstone Golf Club on Saturday to get his third round under way.
Holding a share of the midway lead at eight under par with Australia's John Senden and Geoff Ogilvy and American duo Colt Knost and Tommy Armour III, England's Casey opened with a birdie three to move to nine under.
Playing in a three-player group with Ogilvy and Senden, he bogeyed the par-four third but got back on track with birdies at the fourth and seventh and was 10 under par for the tournament after eight holes when play was halted for the day due to bad light.
That left him one shot adrift of American Bo Van Pelt, who had started at seven under and was at 11 under having played eight.
Play will resume early today at 7.30am local time as PGA Tour officials bid to get the tournament finished on time, although only six of the 79 remaining players had completed their third rounds.
Casey was in a four-way tie for second alongside PGA Tour rookie Knost and Armour III who had also played eight holes, and Fred Couples, who had played 10 holes.
Recovered
Westwood was a shot further back at nine under, four under for his round after 12 holes after holing five birdies and a bogey, include three birdies in a row between nine and 11.
That put the Englishman in a six-man tie for sixth place alongside Sweden's Robert Karlsson, six under in a bogey-free round with one hole to play and Ogilvy who had made consecutive bogeys at the second and third but had recovered with three birdies.
Also at nine under were Americans Jason Bohn, Jonathan Byrd and Ryan Moore.
Ireland's Padraig Harrington had carded a 67 for his second round earlier in the day to get to five under, and after 13 holes of his third round was at eight under for the week in a six-way tie for 12th that also included Henrik Stenson of Sweden and Senden.
Greg Norman will have some time to prepare for his final round on Sunday having finished his third round on Saturday night and the 54-year-old will start at six under par following a two-under round of 70.
England's Brian Davis was also at six under after 12 while Germany's Martin Kaymer was in the clubhouse at five under after a 70.
Ernie Els of South Africa had made amends for an opening 75 with the second-round low score of 66 and he posted a 71 to finish at four under.
Slump
Sweden's Daniel Chopra had holed two late birdies to survive the cut on the line at one under and was making the most of his opportunity, three under for the third round to move to four under after 10.
Sergio Garcia of Spain, Rory McIlroy of Northern Ireland and England's Justin Rose were all going backwards, however.
Garcia had reached the halfway point at four under but had fallen back to two under after 14 holes.
McIlroy, preparing for his Masters debut next week, had already lost ground with a second-round 73 and he had dropped another two shots to fall to two under after 16 holes.
Rose was also in a slump having shot a disappointing, two-over 74 earlier in the day and he was two over for his third round, level par for the tournament after 15 holes.
With the cut coming earlier in the day at one under par, England's Luke Donald, Jeev Milkha Singh of India and Argentina's Angel Cabrera were among those making an early exit from Houston at two over as were Donald's compatriot Greg Owen at three over, Fiji's Vijay Singh and Northern Ireland's Darren Clarke at four over par, and Scotland's Martin Laird, Sweden's Fredrik Jacobson and Argentine Andres Romero at five over.
Alvaro Quiros of Spain's second-round 68 was too little, too late following his opening 83 while world number two Phil Mickelson failed to recover from an opening 77 as he shot a four-over 76 to slide out at nine over par.
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