The Dragons' offense was bogged down for most of the first half, but they rebounded in the second half to advance to the second round against Lovett at 7:30 p.m. next Friday.
Darius Minor, who completed 16 of 31 passes for 255 yards, threw three touchdown passes in the second half to lead the fourth-ranked Dragons (11-0).
Tab Martin was the Dragons leading receiver with five catches for 128 yards and two scores.
"The first half we didn't play up to our potential," Martin said. "We knew in the second half, we had to make a statement and leave no doubt on the field who the best team was. Coosa did a good job, but we finally started going and Darius started finding playmakers."
The victory marks the first time in the school's history that the team has won 11 games.
"Early in the game they were doing a good job against our offensive line," Dragons coach Bill Navas said. "We kind of struggled from that standpoint, but as the game went on that made a difference."
The Eagles (6-5) cut the Dragons lead to three points early in the third quarter when Quentin Hight scored on a 2-yard run. The senior back finished with 13 carries for 154 yards and Shane Smith threw a late touchdown pass with time running out.
The Eagles came into the contest averaging 18 points per game, but turnovers on offense helped keep them out the end zone on a wet night.
"I think we fought hard, but the elements took advantage of us," Coosa coach Chad Perry said. "When you turn over the football against a good team like Jefferson, you're not going to find yourself on the winning end at the end of the game."
Minor put the Dragons on the scoreboard early in the first quarter, when he faked a hand-off to Virgil Appleby and then bounced around the right side for a 15-yard touchdown run.
The Dragons missed out on additional scoring opportunities, moving the ball inside the 20-yard line on four occasions in the first half but coming away with only three points, a 27-yard field goal by Lucas Redd.
Smith ended the Dragons' first possession when he picked off Minor's first pass of the game at the 16-yard line.
"We played sloppy early in the game, and I take the blame for that, because when I play sloppy the offense plays sloppy," Minor said. "We just told ourselves we had to do what we had to do and we did."
Smith, who also starts at quarterback for the Eagles, would have a similar fate when Zac Crosby intercepted his pass, leading to a Dragons' touchdown.
"It was a tale of two halves tonight," Navas said. "To beat Lovett next week, we'll have to put it all together."