The Cardinals won 47-7 in Arizona, with the 49ers' biggest play coming from Hayne who caught a punt and, with the help of blockers, slashed his way for a 37-yard return.
"Jarryd continues to get better every week," Tomsula told reporters.
"He works his tail off."
49ers quarterback Colin Kaepernick had a disastrous game with two of his passes intercepted and returned for touchdowns in the first six minutes.
Kaepernick, signed to a six-year $US114 million ($A162 million) contract, went on to throw two more interceptions and made just nine of 19 passes for 67 yards in what was the worst passing game of his career.
The quarterback took responsibility for the loss, declaring "I nullified the efforts of every other player on that field today".
It was the 49ers' second consecutive big loss after the Pittsburgh Steelers thrashed them 43-18 last week.
"A bad day," Tomsula said.
The only bright spot for Kaepernick was set up by Hayne.
With the 49ers down 28-0 late in the second quarter Cardinals punter Drew Butler booted the ball downfield to where the former NRL star was waiting.
"We had some poor kicking which got them back into the game," Cardinals head coach Bruce Arians, citing the Hayne run as one of the few mistakes his team made, said.
The punt was shorter than expected so Hayne was in full flight when he ran forward to catch it and veered to his right.
49ers blockers in the special teams unit did their job, carving a path for Hayne who sped past two defenders before being shepherded to the sideline.
The return had team-mates on the sideline, with nothing up to that point to cheer for, on their feet and congratulating Hayne with slaps on the back and helmet.
Two plays later, with the 49ers near the end zone thanks to Hayne's run, Kaepernick sprinted for their first and only touchdown.
Just before the game the 49ers announced running back Reggie Bush and punt-returner Bruce Ellington were out with injuries, heightening expectations Hayne would have more time on the field.
However, the 49ers went with chief running back Carlos Hyde, who had 15 carries for 51 yards, and back-up Mike Davis.
Davis, who was ineffective against the Steelers last week, again was easily chopped down and had just six yards from seven carries.
Hayne came on the field as a running back in the second quarter, but didn't carry the ball.
His role was punt-returner, while DeAndrew White, with a fumble, had a mixed game at kick-returner.
The 49ers return to their home field, Levi's Stadium, next week but the undefeated Green Bay Packers will again be formidable opponents.
The Cardinals have started the season 3-0, while the 49ers slip to 1-2.
Share
