Bellamy finished with four catches to lead all receivers.
Mare hit field goals of 44, 51 and 32 yards in the first half before misfiring on a 39-yard attempt off the dirt in the fourth quarter.
Jacksonville's only points came on a safety and a field goal in the third quarter.
The safety occurred when rookie wideout Ernest Wilford blocked Matt Turk's punt through the end zone.
The play was set up by an intentional grounding penalty on A.J. Feeley, which put the Dolphins in a third-and-33 situation from their 2-yard line.
The biggest play on offense came on the next-to-play of the game as Fred Russell broke loose on an 88-yard run.
That came after the Dolphins put together a goal-line stand, with safety Yeremiah Bell knocking down a pass in the end zone on fourth down.
Minor finished with zero yards on five carries, while Morris had 9 yards on four attempts.
At quarterback, both Feeley and Jay Fiedler put up pretty good numbers. Fiedler was 7-for-11 for 89 yards, while Feeley was 8-for-12 for 105 yards. Feeley was intercepted once when his pass for Morris was tipped at the line of scrimmage.
He did lead the Dolphins to a field goal in the two-minute offense, but that was helped by Jacksonville taking a timeout.
The Dolphins seemed content to run out the clock after taking over at their 20-yard line with two minutes left as running plays were called on both first and second down.
But the Jaguars then called a timeout no third-and-5 with 1:09 with the idea of getting the ball back and possibly getting on the scoreboard late.
But Feeley then hit Bellamy for an 18-yard gain to the 43, and the Dolphins then went for the score.
It appeared they had a touchdown when Bellamy got up after making a spectacular diving, one-handed catch and jogged the final 14 yards into the end zone. But officials ruled him down by contact.