The American world number one also carded a 68 to stand four shots off the pace set by Jones on seven-under and a stroke behind big-hitting local Todd Sinnott, who was second after a 70.
Although conditions were markedly calmer than on Thursday, when temperatures soared and gusts of wind swirled across the fairways at the Australian Golf Club, good scores were still at a premium.
Spieth could have really put his stamp on the tournament, therefore, if he had built on the progress he made on the front nine, when he picked up birdies at the first, second and seventh holes.
Another at the 14th sent him to four-under but a poor chip and a short putt at the next saw him drop his first shot of the day, a swipe of the hand in the direction of the offending ball making clear his frustration.
A second bogey at the 16th dropped him deep into the pack again and although he finished with a birdie at the 18th, the 22-year-old was left on three-under feeling he had missed an opportunity.
"The cross-winds again made it a guessing game out there today, leaving a 50-50 shot and we got less than 50 percent of them right," he told reporters.
"It just made it so frustrating as I was striking the ball well, and it was a round I could have shot six or seven under par, and I just didn't have any chances.
"So boy, it was a round that could have been and that made it so frustrating as I found myself finally getting into a nice rhythm as I was hitting fairways and giving myself opportunities but I just couldn't quite gauge the wind."
U.S. PGA tour winner Jones was already in the clubhouse when Spieth got underway, having mixed five birdies with two birdies to add the 68 to the impressive 67 he shot when the wind was at its peak on Thursday afternoon.
The 35-year-old is a member of the host club and conceded that 20 years playing the course gave him some advantage when it came to dealing with the breeze.
"But you've still got to get it in the hole," he said. "If there was no wind, I could have gone out and shot three over today -- that's how golf is."
Belgian Nicolas Colsaerts had the best round of the day with a 66 for a share of third with Spieth, former U.S. Open champion Geoff Ogilvy (71), overnight leader Lincoln Tighe (73) and another local in Aron Price (68).
Former world number one Adam Scott had a rare round where he failed to pick up a single birdie, finishing nine shots off the pace on two-over after a 73.
The difficult conditions means he comfortably made the cut, however, and, like U.S. Open and Masters champion Spieth, will be looking to go low over the weekend.
"Right now I think the goal is going to be to try and shoot 10 under on the weekend and I think that should be good enough," said Spieth.
(Editing by Amlan Chakraborty)
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