Kirk carded a seven-under-par 66 to sit alongside Webb Simpson, Michael Thompson and Jordan Spieth at the top of a congested leaderboard, one clear of four more players on six under.
Kevin Streelman, who headed that group, looked for a long time like he would end the day clear at the top, but unlike many of his colleagues he struggled on the closing holes, dropping shots at 17 and 18.
Kirk was out in three but, after bogeying the 10th, was an unspectacular two under through 13.
A run of five straight birdies catapulted him into the leading quartet, however.
The last five holes were generous to the leaders - Spieth and Thompson each had four birdies in the last five, while Simpson picked up three.
For Streelman it was a different story - he carded eagles at the third and fifth, at which point he was five under, but he bogeyed the sixth and played the last five in one over, putting him down in a share of fifth.
He was joined on six under by Jason Dufner, Zach Johnson and Ryan Moore.
Scotland's Martin Laird was the leading European, in a share of 18th on two under, with only two of the 30-strong field over par.