Tampa Bay, whose four prior victories came on last-gasp scores, didn't need those kind of heroics.
But Mayfield, who has been a revelation early in the season, was plenty impressive.
He threw for 256 yards and two touchdowns, scrambling for a first down late in the third quarter to extend the drive capped by a 45-yard scoring pass to a leaping Tez Johnson - the rookie's first NFL TD.
"Guys just doing their job," Mayfield said. "Young guys stepping up big-time for us.
"I was kind of asleep there for the whole first quarter, but defense kept us in it until I got going - complementary football, that's what it's all about."
The 49ers, already without quarterback Brock Purdy, defensive end Nick Bosa and tight end George Kittle among others, lost linebacker Fred Warner to an ugly right ankle injury in the first quarter.
Warner was carted off a play on which teammate Ji'Ayir Brown rolled onto his ankle.
San Francisco dropped to 4-2, tied in the NFC West with the Los Angeles Rams and Seattle Seahawks.
The Seahawks beat the Jaguars 20-12 in Jacksonville, where Seattle quarterback Sam Darnold's two touchdown passes included a 61-yard bomb to Jaxon Smith-Njigba.
The Rams shook off a slow start with a quick-fire pair of third-quarter touchdowns to beat the reeling Baltimore Ravens 17-3.
It was tied at 3-3 at halftime after the Rams thwarted Baltimore on four attempts to score from less than five yards out, Los Angeles ending the goal-line stand by stopping Derrick Henry on fourth down.
The Rams took the lead on Kyren Williams' three-yard touchdown run early in the third quarter and after Zay Flowers fumbled on Baltimore's ensuing possession, Los Angeles needed just two plays to hit the end zone again on Matthew Stafford's eight-yard pass to Tyler Higbee.
Stafford, who connected on 17 of 26 passes for 181 yards and the touchdown, credited the Rams defense with coming through on a "weird" windy day in Baltimore.
"Obviously (we) fed off our defense and special teams getting the ball back for us a couple of times," Stafford said.
"Just a weird one," he added. "Didn't execute as good as we possibly can, missed some opportunities to score touchdowns in the red zone but found a way to win, which is what matters most."
In their second straight game without injured star quarterback Lamar Jackson, the Ravens fell to 1-5 - extending the team's worst start to a season since 2015 and casting further doubt on their chances of turning things around in time to reach the postseason.
"We're the kind of team that can do it," Ravens coach John Harbaugh insisted, adding that the expected return of Jackson after the team's bye week could be a deciding factor.
"We're going to have healthy players back," he said. "Our quarterback's going to be back. That's a big one."
Cooper Rush's struggles in place of Jackson saw the Ravens send in Tyler Huntley in the fourth quarter.
The Indianapolis Colts continued their strong start, improving to 5-1 with a 31-27 home victory over the Arizona Cardinals -- who saw tight end Travis Vokolek stretchered off early with a frightening neck injury.
Coming off a blowout victory over the Raiders, the Colts had to rally to remain unbeaten at home.
Panthers stun Cowboys
Jonathan Taylor plunged in for a touchdown with 4:32 remaining to put Indianapolis up 31-27 and the Colts defense stymied a potential go-ahead drive by Arizona in which quarterback Jacoby Brissett marched the Cardinals 78 yards but after a third-down sack came up short on an attempt to Trey McBride in the end zone.
Last minute field goals lifted the Carolina Panthers and Los Angeles Chargers to victories, the Panthers shocking the Cowboys 30-27 in Charlotte and the Chargers edging the Dolphins 29-27 in Miami.
Panthers running back Rico Dowdle rushed for 183 yards with 56 receiving yards and a touchdown against his former team and Ryan Fitzgerald booted the game-winning field goal on the final play.
"They wasn't buckled up," Dowdle said of a Dallas team that let him depart as a free agent after last season.
Chargers quarterback Justin Herbert escaped pressure to hit Ladd McConkey for a 42-yard gain and set up Cameron Dicker's fifth field goal, a 33-yarder with five seconds left to seal their win.
The day's action started in London, where the Denver Broncos sacked New York Jets quarterback Justin Fields nine times on the way to a 13-11 victory.
The Broncos trailed 11-10 after giving up a safety in the third quarter.
But Wil Lutz's 27-yard field goal with 5:06 remaining put them back in front and Jonathon Cooper and Justin Strnad sacked Fields to seal a win that dropped the Jets to 0-6.