Spieth has won 11 times on the PGA Tour but is hoping to end a lengthy dry spell dating back over three years to the 2017 British Open.
His game has been trending in the right direction with the Masters looming at Augusta National next week.
The 27-year old American highlighted that with a stellar back nine to get to 12-under 204 and a tie with England’s four-time European Tour winner Wallace, who also shot a 67.
“I left the ball in the right spots when it was missed and really, I did a great job managing today,” he said.
Former winner Charley Hoffman shook off a slow start to the week at one of his favourite events on the Tour and was firmly in contention at San Antonio.
Hoffman fired a seven-under 65 for a 10-under total of 206.
Like Spieth, Hoffman caught fire on the back side at TPC San Antonio, with an eagle on No. 14 and three straight birdies to cap his round.
Cameron Tringale was alone in fourth place at eight under, while India’s Anirban Lahiri rounded out the top five after a 69 to reach seven-under, five shots off the lead.
The tournament returned this week after being cancelled in 2020 due to the Covid-19 pandemic. It is one of the longest running events on the Tour and was first held in 1922.
Texas native Spieth has three top four finishes in his last six starts and a win Sunday would be a confidence-booster for the Masters, which he won in 2015.
He had an uneventful front nine with one birdie and a bogey on No. 9 before kicking his game into high gear with a birdie on the par-four 12th. He then two-putted for birdie on the par-five 14th and drained a six foot putt on 15 to get to 10 under.
After a par on 16, Spieth made one of his best shots in the tournament on the 308-yard, par-four 17th. He hit his tee shot wide right, then perfectly executed a flop shot from just off a gravel path to within three feet of the pin to get to 11 under.
He tacked on another birdie on 18 with a 321 yard drive down the right side of the fairway then landed his approach in the middle of the green. He finished off the round with a tap in birdie and a big smile.
Playing alongside Spieth, Wallace kept pace with back-to-back birdies to close out his 67 round. He also tapped in for birdie on the final hole.
“Started off lovely,” said Wallace, who is looking for his first win in the United States. “I felt nervous, but that’s a good thing because I haven’t been in this situation in a while.”
Hoffman was also in a zone Saturday on the back nine with an eagle and four birdies on his last seven holes.
The Texas Open has been his personal playground over the past decade as he is the tournament’s all-time earnings leader while making the cut in his last 11 starts. Hoffman won the event in 2016 and has a pair of runner-up finishes.
He has yet to qualify for the Masters so there is plenty of extra motivation for Sunday.
“It was good fun on the back nine, trading birdies,” Spieth said. “I think that’s what we’ll hopefully look to do tomorrow. On the back, it was nice to see some putts go in within the group. It was a fun atmosphere out there.”
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