Allenby claimed victory here in 2000, when he defeated PGA Tour veteran Craig Stadler on the fourth extra hole of sudden death, after finishing at 13-under 275.
The victory marked the 29-year-olds first win on the American tour.
However, Allenby was apparently not satisfied with just one, as he quickly claimed another triumph later in the year at the Advil Western Open, this time in a playoff win over another PGA Tour veteran Nick Price.
In this 2001 season, he has shown that last years performances in the United States were no flukes, as he has already captured another win.
This one occured at a rainy, cold Riviera Country Club, site of one of the biggest events of the season, the Nissan Open. It also ended in a playoff, with Allenby getting the better of five others on the first extra hole.
Allenby will not have an easy time of defending this time around, however.
Several other of his native countrymen are scheduled in the field, including PGA Tour Q-school champion Stephen Allan, Stuart Appleby, Steve Elkington and youngster Adam Scott.
Others set to tee it up include Lee Janzen, Hal Sutton, Vijay Singh, Fred Couples and Joe Durant.
The Houston Open has been contested at The Woodlands since 1975. Winners at this venue have included the likes of Raymond Floyd, Payne Stewart and Gary Player.
Before the move in 75, the event was hosted at a number of different stops leading all the way back to 1946, when Byron Nelson took the inaugural event by two shots over Ben Hogan at River Oaks Country Club.
Prize money for the victor was not much then, but the winner this year will find himself $612,000 richer.
See who is in this week's field