The 31-13 victory at TIAA Bank Field in Jacksonville, Fla., was the Dolphins' first win of the season. Fitzpatrick completed 18 of 20 passes for 160 yards for Miami.
"I felt like we were efficient," Fitzpatrick told reporters. "We had a good game plan. We followed it. Guys made plays.
"[We were] running the clock out a little bit in the second half, but I thought our guys came to play."
Fitzpatrick completed a franchise-record 90% of his attempts in the victory.
The 37-year-old veteran quarterback orchestrated a 12-play, 84-yard touchdown drive to start the game. He threw a 3-yard touchdown pass to Preston Williams to give the Dolphins a 7-0 advantage with 8:15 remaining in the first quarter.
Running back Jordan Howard capped off Miami's next drive with a one-yard rushing touchdown, for a 14-0 advantage with 2:41 remaining in the quarter.
Jaguars running back James Robinson cut the Dolphins lead in half with a 11-yard rushing touchdown at the start of the second quarter.
The Dolphins then scored on their third consecutive drive when Fitzpatrick hooked up with tight end Mike Gesicki with a 15-yard touchdown pass. Miami led 21-7 at halftime.
In the second half, the Dolphins took a 28-7 advantage when Fitzpatrick scored a one-yard rushing touchdown with 2:05 remaining in the third quarter.
Robinson returned to the end zone for another Jacksonville score two drives later with a one-yard rushing touchdown to make it 28-13 with 9:07 left in the game.
Dolphins kicker Jason Sanders made a 30-yard field goal with 3:54 remaining for the final points of the night.
"We had too many mistakes, it's plain and simple," Jaguars quarterback Gardner Minshew said. "No matter what the score is, we should be able to go out there and execute and we just didn't do a good enough job of that."
Minshew completed 30 of 42 passes for 275 yards and an interception in the loss. Robinson had 129 yards from scrimmage and two scores on 17 touches for Jacksonville.
Dolphins running back Myles Gaskin had 95 yards from scrimmage on 27 touches. Linebacker Kyle Van Noy had a sack, a forced fumble and a fumble recovery in the win. Kamu Grugier-Hill and Andrew Van Ginkel also had sacks for the Dolphins.
"It wasn't just Fitzpatrick," Dolphins coach Brian Flores said. "There are 11 guys on each snap. ... We got contributions from a lot of different guys -- the offensive line, the backs, tight ends, receivers -- everyone contributed and that is what you need to win in this league."