The 40-year-old Australian produced a stunning eight-under-par 63 at the Mines Resort and Golf Club to lead by one shot from playing partner, Jhonattan Vegas of Venezuela.
Sweden's Fredrik Jacobson carded a 65 for third place while Asia's best performers were Thai star Thongchai Jaidee and Bangladeshi trailblazer Siddikur, who returned rounds of 68s for tied 12th position in the event sanctioned by the Asian Tour and PGA Tour.
Allenby, a four-time winner on the PGA Tour, continued to show his liking for the Mines Resort with eight birdies on the card, including three on the trot from the 15th hole. In last year's inaugural CIMB Asia Pacific Classic, Malaysia, Allenby closed the week with a 64 for equal fifth place.
"I'm obviously very happy with the way I played. I made a lot of nice putts and hit the ball really well all day. I had just one wayward tee shot, at the last but I made a good par save," said Allenby, who recorded his first pro win at the 1992 Perak Masters in Malaysia.
With his last win being the 2009 Australian Masters, Allenby is keen to return to the winner's enclosure in Malaysia, which would also give him a timely boost as he will compete in the Presidents Cup as a captain's pick on his home course, the Royal Melbourne next month.
"I've been playing well for a while, but I just haven't really put the scores on the board. I've been making a lot of birdies, but a few others have been slipping in there. So to have a bogey-free round and to shoot eight-under around here is a great score," he said.
"I like the course. It sets up really well for me. There are holes where you can drive the ball long and straight, but there are also a lot of holes where you have to have good iron play. My iron play was very solid today [Thursday]. I think more importantly is I made a lot of good putts as well. That's probably been the part [of my game] that has been letting me down of late. I've been working hard on it, and I'm starting to make some putts and hope that's where it is for the rest of the tournament."
Vegas, who won earlier in the year on the PGA Tour in what is his rookie season, stayed in touch with Allenby with a magnificent finish where he birdied his last four holes. "I had a really good round. Hopefully we can keep that going for the next three days and hold the trophy on Sunday," said the Venezuelan.
"I hit the ball beautifully. I kept hitting on the fairways and the greens, made some good putts and finished with four birdies in a row which was a nice way to end the round.
"Winning earlier in the year was like a dream come true. I feel like I'm starting to play well again like how I did earlier in the year which is nice."
Jacobson, who won his first PGA Tour title this year at the Travelers Championship and is a former champion of the Hong Kong Open, soared on eagle's wings when he holed a bunker shot at the short par four 15th hole.
"I hit a perfect bunker shot. That was a bit of a nice one to get. It was 25 yards, with the bunker a little left of the green. If I could have upped-and-downed it from there I would have been really happy. But I got a good look at it," said the Swede.
Scores after round 1 of the CIMB Asia Pacific Classic Malaysia being played at the par 71, 6917 Yards The Mines Resort GC course (a- denotes amateur):
63 - Robert ALLENBY (AUS).
64 - Jhonattan VEGAS (VEN).
65 - Fredrik JACOBSON (SWE).
66 - Cameron TRINGALE (USA), Jimmy WALKER (USA), Bo VAN PELT (USA).
67 - Scott STALLINGS (USA), Stewart CINK (USA), Jeff OVERTON (USA), Mark WILSON (USA), John SENDEN (AUS).
68 - Tommy GAINEY (USA), Brendon DE JONGE (ZIM), Carl PETTERSSON (SWE), Rory SABBATINI (RSA), Kyle STANLEY (USA), Thongchai JAIDEE (THA), Mohd SIDDIKUR (BAN).
69 - Charley HOFFMAN (USA), Ben CRANE (USA), Jerry KELLY (USA), Ricky BARNES (USA), Camilo VILLEGAS (COL), Jonathan BYRD (USA), Jeev SINGH (IND), Chez REAVIE (USA).
70 - Spencer LEVIN (USA), Chinnarat PHADUNGSIL (THA), Kiradech APHIBARNRAT (THA), Jason DUFNER (USA), Jbe KRUGER (RSA), Tetsuji HIRATSUKA (JPN).
71 - D.A. POINTS (USA), Ryan PALMER (USA), Chris KIRK (USA), Lucas GLOVER (USA), Brian DAVIS (ENG), Ryan MOORE (USA), Danny CHIA (MAS), Brandt SNEDEKER (USA).
72 - Stuart APPLEBY (AUS), Shaaban HUSSIN (MAS), CHAN Yih-shin (TPE), Vijay SINGH (FIJ).
73 - Angel CABRERA (ARG), David GLEESON (AUS).
74 - Brendan STEELE (USA).
75 - S.S.P. CHOWRASIA (IND).