Jonzon, 24, who almost failed to retain his European Tour card last year, changed his putter this week and picked up seven birdies - including putts of 30 feet and 20 feet - on his way to a two-round total of 132.
The defending champion, Wayne Riley of Australia, had six birdies as he shot a 66 to stand two strokes back at 134. Also at 10 under was the first-round leader, Peter O'Malley of Australia, who had a 69.
Jose Maria Olazabal, continuing his remarkable comeback after an 18-month lay-off due to a foot ailment, returned a 67 to lie five shots off the lead on 137.
Ballesteros, Europe's Ryder Cup captain, shot a 72 for a half-way total of one-over-par 145. "Things didn't go the right way," said the Spaniard, who hooked off the tree-lined course three times. "I didn't manage to have a stable round and that's it."
The misery continued for Scotland's Sam Torrance, who improved on his opening 81 by 11 shots but still bowed out with a seven-over-par aggregate of 151.
Colin Montgomerie made a solid start in the Honda Classic at Coral Springs, Florida, shooting 68 Thursday to stand one shot off the pace in a group of five players. Lee Janzen and Paul Stankowski shared the lead.
Both Janzen and Stewart had a preview of the new TPC at Heron Bay course, designed by their fellow PGA Tour player, Mark McCumber. "I was excited about coming here and playing. I thought it would be a fair test, even if the wind blows," Janzen said.
The wind did blow during the first round, and scores were higher than expected on this flat course with no out of bounds and almost no water.
"There's more to this course than we first thought," Montgomerie said. "Suddenly the pins were tucked away and we were playing in tournament conditions. It was tough out there.
"I don't mind it blowing. In fact, what that does is take away the 63s and 62s, but it doesn't stop people from scoring 67s and 68s."
A headwind certainly stopped most people from picking up shots at the last. It produced an average score half a stroke above its par of four.Reuse content