Mallinger, whose lone PGA Tour victory came at the Pebble Beach Invitational two years ago, highlighted his round with an eagle at the par-5 15th on his way to a 30 on the back nine of the CordeValle Golf Club course.
He stood at 14-under 128 for 36 holes with Billy Horschel and Jhonattan Vegas sharing second place at 132.
Those at 133 included Nicolas Colsaerts, Scott Dunlap and first-round leader Nick O'Hern, who followed his opening 62 with an even-par 71.
Colsaerts, a member of European team that won the Ryder Cup last month, took a large stride toward becoming a full-time competitor on the PGA Tour.
He accepted a special temporary membership to the tour earlier this year, which meant he was able to receive unlimited sponsor exemptions for the rest of 2012. In eight tour starts this season, three of them in World Golf Championship events, he has earned $652,886.
In order to become a full-time tour member for next year, he must finish among the top 125 money winners and the player currently in 125th place (Jeff Maggert) has accumulated $598,994.
A high finish this week by Colsaerts will all but clinch his spot in the top 125 with two tournaments remaining on the 2012 schedule.