Jerry Kelly and Bob Estes each posted rounds of 4-under 68 to finish tied for third at 12-under-par 204. Second-round leader John Cook carded an even-par 72 to finish alongside Davis Love III (68) at 11-under-par 205.
Allenby began the day three strokes off the lead and kept pace as several players jammed the top of the leaderboard. He picked up two birdies over his first five holes to climb to 10-under, but ran into trouble with a bogey at the par-3 sixth after he found a bunker off the tee.
The Aussie responded with back-to-back birdies from the eighth to move into a share of the lead at 11-under with Joe Durant, Jerry Kelly and good friend and fellow countryman Stuart Appleby,
Neal Lancaster soon took a share of first with three straight birdies from the eighth as Kelly faltered with a bogey at the 11th. Durant also found trouble on the back nine, falling from the top spot with a double bogey at the 11th and a bogey at the 13th.
Lancaster took the outright lead with back-to-back birdies from the 14th to reach minus 13, while Appleby's round fell apart. Appleby missed the green with his approach at the 13th and watched as his ball rolled down a slope and into the woods.
He chipped out to the rough and found the green with his fourth shot, then failed to convert from seven feet for bogey. Things didn't get better for Appleby, who followed the double bogey with a bogey when he missed a three-foot par save at the very next hole.
Allenby remained within one of Lancaster then leap-frogged the leader thanks in part to a tremendous drive at the par-5 15th. With a clear approach from the fairway, Allenby landed his second shot onto the putting surface and drained a 15-footer for an eagle and the outright lead.
At the 16th, Allenby knocked his approach within eight feet of the hole for birdie to add to his advantage.
'I was trying to make a birdie on 16 just to keep the momentum going,' said Allenby. 'A lot of times when you make eagles, you don't back it up with a good hole, so I thought it was important to get a good tee shot away and hit a great second shot in there and make a good putt, and that's what I did.'
He parred the remaining two holes to take a solid margin into the final round in search of his second Western Open title at Cog Hill Golf & Country Club's Dubsdread Course.
'My game is just slowly getting better and better as the year goes along,' said Allenby. 'I feel like it's just gotten better since the U.S. Open, just gained a lot more confidence with my game.'
Allenby, 30, captured this event in 2000 after surviving a playoff with two-time Western Open champ Nick Price, but missed the cut last year. He has earned three other PGA Tour titles, including two others in playoffs, and is eager to earn his first victory of 2002.
'I think maybe last year I was just too confident,' Allenby said of his Western Open performance a year ago.
Appleby never recovered from his blunder at the 13th en route to a round of 71. The 31-year-old finished at 10-under-par 206 alongside David Frost, Chris Riley, Duffy Waldorf and Scott Verplank.
Bob Tway, who shared low round of the day honors with Allenby with a 65 of his own, finished tied for 12th with Price, John Senden, Brandt Jobe, Paul Gow and Vijay Singh at 9-under-par 207.
Full-field scores from the Advil Western Open