Green Bay missed out on a chance to clinch a playoff spot.
Giving Tennessee (6-7) a potent running game it has lacked all season, Hicks scored on a 22-yard run with 10:42 left and iced the victory with a 51-yard run that enabled the Titans to run out the clock.
The fourth-year pro from UCLA was used as the primary back instead of the slumping Eddie George and became the first Tennessee runner to reach 100 yards this season.
"We were out there just playing ball and that made it fun for all of us," Hicks said. "It was just a matter of time before we got the running game going and I just happened to be in the game when we got it going."
Green Bay (9-4) posted an emotional 17-7 victory over the Chicago Bears at Lambeau Field last week to move into a first-place tie in the NFC Central. But the Packers fell behind the Bears (10-3), who beat Tampa Bay on Sunday.
A victory by the Packers plus losses by Tampa Bay, Atlanta and Washington would have put Green Bay in the playoffs. The Buccaneers, Falcons and Redskins all lost, but Green Bay could not hold up its end.
"We did not have a letdown today. They just made more plays than us. They were able to penetrate and stop the run," Packers coach Mike Sherman said. "This is not a shocker. They have a lot of talent over there in that locker room."
Brett Favre threw a pair of touchdown passes for the Packers, but completed just 21 of 39 with two interceptions and had a costly fumble.
While Hicks ran wild, Ahman Green of the Packers was held to just nine yards on nine carries.
Ryan Longwell kicked a pair of field goals for Green Bay, including a franchise-record tying 54-yarder to close the first half.
The Titans won for the 10th time in their last 11 games against NFC foes and trail the New York Jets (8-5) by two games for the third and final AFC wild card berth.
The day started poorly for Green Bay. A 70-yard punt by former Packer Craig Hentrich was downed at the Green Bay one and Green was tackled in the end zone on the next play.
The Packers answered with a 33-yard field goal by Longwell before defensive end Vonnie Holliday sacked McNair and recovered the quarterback's fumble at the Tennessee 21.
Four plays later, Favre found Donald Driver over the middle for a seven-yard touchdown pass to give the Packers a 10-2 lead.
McNair had his way with the Green Bay secondary on the next possession, completing four passes of at least 10 yards before a four-yard touchdown pass out of the backfield to Green. A two-point conversion failed, keeping the score at 10-8.
Later in the quarter, it was Tennessee's turn to capitalize on a turnover. Jevon Kearse forced a fumble by Favre and McNair threw a touchdown pass to Mason on the next play to put the Titans in front, 15-10.
"Kearse played a Pro Bowl type of game today and had pressure on us all game," Sherman said.
McNair maintained his touch in the third quarter, completing passes of 25 and 24 yards to tight end Frank Wycheck that led to a 24-yard field goal by Joe Nedney.
Hicks increased the lead to 26-13 with his touchdown run with 10:42 left, breaking tackles along the way.
Favre cut the deficit to seven points with a 16-yard pass to Bill Schroeder with 6:42 left, but Green Bay would get no closer. Schroeder caught six passes for 82 yards.
The Packers lost for the first time in seven December games.