The Australian hit five birdies and was five under par through 11 holes to hold a share of the overall lead on nine under.
Allenby picked up shots at the first, third, fourth, 10th and 11th to join Bae Sang-moon, Marc Leishman and Chris Kirk at the top of the leaderboard.
Bae of South Korea, who shot a brilliant 63 in round one before following it with a 70, was two under through six thanks to birdies at the second and third.
American Kirk was also two under after six, while Leishman, another Australian, was level par through five.
There were a group of six players a shot further back, including American John Peterson, who was the biggest climber so far, five under through 13.
Jason Dufner, Greg Chalmers, Jerry Kelly, Jason Kokrak and Brian Stuard were also on eight under.