The Tigers scored 40 points by winning the final event, the 400 freestyle relay, to finish with 730.5 points to 700 for Florida, which finished second in the relay and second on the scoreboard.
The Tigers show off their championship trophy on Saturday night in Knoxville.
In the women's competition Auburn finished fourth. Georgia won the title with 781 points, Tennessee was second with 629.5 followed by Florida with 566 and Auburn with 509.5 points.
"This is the third straight SEC meet where it has come down to the last relay," Auburn head coach Brett Hawke said of the men's team victory. "It's a really competitive conference.
"We had a lot of great swims," Hawke said. "We had to dig deep tonight because it's not easy. This is a great group, and they know how to respond on the last day when it counts the most."
The Auburn men and women combined for four wins on on Saturday night with both finishing the meet with victories in the final event.
The men's 400 freestyle relay team of Drew Modrov, James Disney-May, Kyle Owens and Marcelo Chierighini gave Auburn its ninth title in the last 10 years in the event with a time of 2:51.66. Auburn's men team won all five relays during the week.
Led by senior Olympian Arianna Vanderpool-Wallace, the women's team won the 400 freestyle realy. Swimming the leadoff leg she broke her own SEC and NCAA record in the 100 freestyle with a time of 46.61, 0.20 of a second under her time from last year's SEC meet. It gave the relay team of Vanderpool-Wallace, Hannah Riordan, Megan Fonteno and Haley Krakoski big lead as they won in an NCAA ‘A' cut time of 3:12.85.
"I had a lot of emotion going into that race," Vanderpool-Wallace said of her final SEC race. "I just wanted to go out and get the women into open water. That and the emotion led to breaking the record. It's awesome, and I know I can go faster. This year is about getting everything right and going faster at NCAAs."
Kyle Owens swims the backstroke for the Tigers.
Owens earned two wins on the night. In addition to his relay victory, he took first place in the 200 backstroke with a time of 1:41.67. He led a 1-2 finish in the event as senior Max Murphy clocked a 1:42.59 to finish second.
Auburn took the lead after the 200 backstroke and never gave it up.
"We get in there--Brandon, Max and me--and we train together every day," Owens said. "We said back in September that it was going to come down to this. And we know Auburn has the best backstroke in the country."
Owens was part of four winning relay teams and won two individual events for the Tigers.
"It was just an extraordinary effort," Hawke said. "Sixteen in a row for us is just hard to believe. The team worked so hard, and the coaching staff put in numerous hours putting this together. When it comes together like this, it's just a great feeling."