Kevin Jurovich caught seven passes for 135 yards and two TDs for the Spartans (2-3).
Dick Tomey, notched his 304th career victory to move into a tie with Jackie Sherrill for 23rd place on the all time career list.
Tafralis, was 12 of 14 in the first half and finished 25 of 34.
"There's a world of difference," defensive end Jarron Gilbert said. "Now we're stacking wins and trying to turn the season around. Being 0-3 hurt bad. We know what losing feels like. We don't want that feeling anymore."
The Spartans rushed for just 15 yards on 26 attempts against UC Davis and are averaging only 54.5 yards on the ground over the last four games.
The four touchdowns against the Aggies moved Tafralis into fifth place on the Spartans' career passing list.
"There are coaches all over the country who would love to have a win where they didn't quite do everything as you would like," Coach Dick Tomey said. "It's not going to be pretty most weeks. We're going to have to scratch and claw for everything we get."
"We know we can pass, we've proven it the past two weeks," said Tafralis, who completed 25 of 34 attempts a week after the passed for a career-high 426 yards and three touchdowns at Utah State. "But we need to get a running game going. That is a big, big thing for us. If we want to be a good team we've got to be able to run the ball."
"We were up seven, but when I walked off the field I sure felt like I was losing," Tafralis said. "I felt like we were being outplayed. They were beating us up up front, and we just weren't converting on things we needed to.
"But the second half we came out strong."
"We woke up," after UC-Davis scored on its opening drive, said cornerback Dwight Lowery, whose second-quarter interception stalled an Aggies drive. "I personally didn't feel 100 percent ready on that drive. After that, we just played better."
San Jose State won at home for the ninth time in 10 games, and play again at home versus Idaho for a homecoming tilt.
We look forward to seeing you all there!
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