The heavyweight clash capped the final day of the NFL regular season, which also saw the Denver Broncos and Tampa Bay Buccaneers claim the final two playoff places available.
The Lions ended the first half with a 10-6 lead thanks to a first quarter 25-yard rushing touchdown from Gibbs.
Will Reichard's third field goal of the game brought the Vikings within a point but then the Lions offense sprang to life with 21 unanswered points.
Gibbs collected a 10-yard pass from quarterback Jared Goff and then made sure of Detroit's 15th win of the season with a pair of fourth quarter rushing touchdowns.
The Lions will have a bye in the first round of the playoffs and home field advantage throughout while the Vikings travel to the Los Angeles Rams in next week's wildcard round.
Gibbs put up 139 yards on the ground and 31 receiving yards on five catches.
Denver claimed the final berth on offer with a 38-0 win over a weakened Kansas City Chiefs, ending their nine-year playoff drought.
The Chiefs, the defending Super Bowl champions, had already secured the top seed in the AFC and they rested quarterback Patrick Mahomes, tight-end Travis Kelce and several other regular starters.
Inevitably, that made things much easier for the Broncos, who knew victory would secure them a playoff place regardless of results elsewhere. The Broncos face a tough test in the wildcard round, however, where they will be at second-seeded Buffalo Bills.
The Broncos win ended Cincinnati's hopes despite the Bengals' victory over the Pittsburgh Steelers on Saturday. The Miami Dolphins were also eliminated.
Denver's rookie quarterback Bo Nix threw for 321 yards and four touchdowns and added 47 yards on the ground in a win that was basically assured after they took a 24-0 lead in the first half.
The Tampa Bay Buccaneers also took their place in the playoffs, winning the NFC South division thanks to a 27-19 victory over the New Orleans Saints.
The win for Tampa Bay,which set up a clash with the Washington Commanders, denied Atlanta a place in the playoffs as Falcons dropped their final game 44-38 to the Carolina Panthers.
The Buccaneers trailed 19-13 going into the fourth quarter before quarterback Baker Mayfield, facing a three-man rush, stepped out of the pocket and delivered a brilliant 23-yard touchdown pass to Jalen McMillan.
Bucky Irving then wrapped up the win with an 11-yard rushing score with 1:51 left in the game.
Mayfield threw for 221 yards and two touchdowns while receiver Mike Evans had 89 yards receiving, taking him past the 1,000-yard mark for the 11th straight season.
The Commanders, already in the post-season, took the sixth seed in the NFC with a 23-19 win over the Dallas Cowboys.
With only playoff seeding on the line, the Commanders replaced rookie quarterback Jayden Daniels at the half trailing 6-3 to Dallas.
But back-up Marcus Mariota came in and threw the game-winning touchdown, a 5-yard pass to Terry McLaurin with just three seconds to play.
The Green Bay Packers, already assured of a playoff spot, suffered injuries to quarterback Jordan Love and wide receiver Christian Watson in a 24-22 loss to the Chicago Bears.
Watson suffered a knee injury in the second quarter and Love followed shortly afterward with an elbow problem which was later described as a precautionary move by coach Matt LaFleur.
The Packers will face the second-seeded Philadelphia Eagles in the wildcard round.
Titans get No.1 pick
The Tennessee Titans will have the number one draft pick after they lost 23-14 to the Houston Texans while the New England Patriots beat the Buffalo Bills 23-16.
The Patriots would have had the first pick had they not pulled off the upset win over a playoff-bound Bills team that gave quarterback Josh Allen just one snap before he was replaced.
Shortly after the game, Patriots owner Robert Kraft fired first-year head coach Jerod Mayo.
Aaron Rodgers became just the fifth quarterback in NFL history to throw 500 career touchdowns, reaching the milestone during his New York Jets' 32-20 win over Miami.
Rodgers, whose future is unclear, threw for 274 yards and four touchdowns in the win for the 5-12 Jets.
