Casey completed 54 holes at 19-under-par 197. His three-round total broke Martin Kaymer's record of 199, which the German set last year. Casey, an eight-time winner on the European Tour, collected his last title at this event in 2007.
Kaymer, the defending champion, fired a 7-under 65 to move into second place at 15-under-par 201.
Englishmen Graeme Storm and Anthony Wall are alone in third and fourth. Storm, who shared the lead after the second round, carded a 3-under 69 and stands at 14-under-par 202. Wall also shot 69 and is one stroke further back at minus-13.
The tournament is back on track after the second and third rounds were completed Saturday. There was a two-hour delay during the first round that pushed the tournament back.
Casey got off to a quick start with birdies on one and two. After four straight pars, he birdied the par-3 seventh at Abu Dhabi Golf Club to move to 13 under.
The Englishman then picked up his third birdie in three days at the par-5 eighth. He also birdied the par-5 10th thanks to a 40-foot birdie putt.
'That was the turning point, I think,' said Casey, whose drive on 10 was under a tree. 'On the second shot, I didn't know where the ball was going to go and I didn't know whether I would break my club.'
Casey kept rolling with back-to-back birdies from the par-three 12th. He parred three in a row from the 14th, but closed with a flourish.
The 31-year-old birdied the 17th get to 18 under, then birdied the par-5 18th for the third consecutive day to set the new 54-hole scoring record by two strokes.
'I didn't expect much after (Friday's) 65. It was nice playing with Graeme, who is actually a good friend,' stated Casey. 'We all got off to a great start. I think it's always enjoyable to shoot 63'
Kaymer opened with six straight pars before making birdie at No. 7. He then eagled the par-5 eighth to jump to 11 under.
Around the turn, Kaymer dropped in back-to-back birdie efforts from the 11th and again from the 17th to move into second place.
'I think it's going to be a totally different situation for me,' said Kaymer in comparing last year's final round with Sunday's finale. 'I was in the lead by six shots last year when I went out on Sunday, and it was a similar situation. It's going to be very new for me.'
Peter Hanson fired a 6-under 66 to climb into a share of fifth at 12-under-par 204. He was joined there by Louis Oosthuizen (68) and Johan Edfors (69).
Padraig Harrington, the reigning British Open and PGA Championship winner, is part of a group tied for eighth place at minus-11. He stands alongside Oliver Fisher (69), Stephen Gallacher (65) and Danny Willett (68).