Anthony Painter, who held the opening-round lead, managed an even-par 71 to finish at 6-under-par 136. He was joined by Jens Nilsson, who posted a 69, and Paul Gow, who fired a 65, in a tie for second.
Groom began the day one shot off the pace at Kooyonga Golf Club and stumbled out of the gate with a bogey at the opening hole. He countered with a birdie at the par-3 third and added another birdie at the par-4 sixth to reach 6 under.
'I guess on the first tee you feel a bit of pressure,' said Groom. 'But once you get going you don't worry about it.'
The 25-year-old faltered with a bogey at the par-4 eighth to return to minus-five but Groom made a push down the stretch.
The Australian picked up a birdie at the par-4 16th and closed with a birdie at the last to grab hold of the outright lead.
'First things first, I've got some work to do over the weekend,' said Groom, who is playing under a sponsor's exemption. 'I can't get ahead of myself.'
Painter quickly relinquished his overnight lead with back-to-back bogeys starting at the second but he responded with consecutive birdies from the fifth.
The 38-year-old dropped another shot at the eighth but was able to recover again with a birdie at the very next hole.
Painter moved to 7 under with a birdie at the 12th but found trouble with a bogey at the 14th to finish one shot back.
Gow played the back side first and collected a pair of birdies over his first nine holes.
The 33-year-old, who is a two-time winner on the Nationwide Tour, added four birdies on the front half for his share of second.
Brendan Jones and Euan Walters finished in a tie for fifth place at 5-under-par 137.
Nathan Green, Nick O'Hern, Wayne Grady, Vance Veazey, Paul Sheehan, Brett Wetterich and Bob Sowards were three shots off the pace at 4-under-par 138.
The 36-hole cut fell at 2-over-par 144 with 67 players qualifying for the weekend. Among those who failed to make the grade were Peter O'Malley, Ty Tryon and Greg Chalmers.