Robbie Gould, who missed a potential game-winner earlier in overtime from just 37 yards out, connected on a 25-yard field goal with 3:37 left to give the Bears a harder-than-expected victory.
The win, coupled with Washington's upset of New Orleans, clinched home-field advantage for the Bears (12-2). The NFC North champions had already earned a first-round bye the week before.
Gould's field goal came after Davis made an incredible twisting-and-turning 28-yard catch on a 3rd-and-8 pass from Rex Grossman to get the ball to the Tampa Bay 20.
Two plays later, Peterson, Chicago's third-team tailback, powered the ball to the 7-yard line with a punishing 11-yard rush up the middle.
Trailing by three TDs in the third quarter, the Bucs (3-11) stunned the Bears with three fourth-quarter touchdowns, tying the game on Tim Rattay's 44-yard scoring strike to Ike Hilliard with 3:44 left.
Tampa Bay ended a 13-quarter drought without a touchdown when Joliet native Mike Alstott scored on a 14-yard run with 25 seconds left in the third quarter.
That made it 24-10, and just moments later, the Bucs got back in the game when Bears' rookie kick return star Devin Hester - who had two return touchdowns last Monday - fumbled the ensuing kickoff after a hit by Blue Adams with Wesly Mallard recovering at the Chicago 16.
Rattay hit Alex Smith with a 9-yard TD pass early in the fourth, and suddenly the supposedly down-and-out Bucs were within a touchdown.
But Grossman, who finished 29-of-44 for 339 yards, hit four straight passes on a 77-yard drive, highlighted by an 18-yarder to Desmond Clark. Cedric Benson's 4-yard TD run made it a two-touchdown advantage with 9:23 to go.
The game certainly seemed to be in hand, but the Bears couldn't get the Bucs to go away.
Clark caught seven passes for 125 yards and a pair of touchdowns, all but one of the receptions coming in the first half when the Bears built a 21-3 lead.
Clark set a new career high in receiving yards and is the first Bears tight end to crack the century mark since Emery Moorehead in 1985.
Bears starting nose tackle Tank Johnson, arrested Thursday for possession of firearms without a Firearm Owner's Identification card, was inactive for the game. Early Saturday morning, Johnson was at a downtown Chicago nightclub when his alleged bodyguard and childhood friend, Willie B. Posey, was shot to death during a fight.
Johnson was told to stay home and was not present at Soldier Field on Sunday.
Hester, who has an NFL-record six returns for TDs this season, lined up as a wide receiver for the first time this season late in the first quarter, but Grossman's pass to him on the left side was too way low and incomplete. Hester fumbled three times on kicks, losing just one.
Get Chicago Bears Tickets at The Ticket Chest