It was the second time this month that Folk was called upon to kick a last-second field goal for the win. His 51-yard kick pushed the Patriots past the New York Jets 30-27 on Nov. 9.
James White also helped keep the Patriots' (5-6) playoff hopes alive with two rushing touchdowns. He finished with five rushes for 18 yards and the two scores.
Patriots quarterback Cam Newton struggled once again, completing 9 of 18 passes for 84 yards and two interceptions. He added nine carries for 46 yards in the victory over the Cardinals.
"I'd rather have an ugly win than a pretty loss," Newton said. "We didn't play our best game offensively. But when we needed it, we got the job done and that's all that counts."
The Patriots' defense limited the Cardinals' top-ranked offense to 298 total offensive yards. New England also had a pivotal goal-line stand before halftime that kept its deficit to only three points to start the second half.
Cardinals quarterback Kyler Murray finished 23 of 34 for 170 yards and an interception. He had 31 rushing yards and was held to zero touchdown passes for the first time this season.
Kenyan Drake had 78 rushing yards and two touchdowns on 22 carries for the Cardinals (6-5). DeAndre Hopkins finished with a team-high 55 receiving yards on five catches.
The Cardinals are scheduled to host the Los Angeles Rams next Sunday, while the Patriots will visit the Los Angeles Chargers.