Lions quarterback Jared Goff twice thought he had delivered a winning touchdown in the game's final seconds, only for both to be ruled out for offensive pass interference, sparking furious scenes at Ford Field.
"Crazy game...so happy to get a win," said Rodgers, describing the high-stakes clash's final moments as "chaos."
Pittsburgh's win means the Chicago Bears and the San Francisco 49ers are guaranteed for the NFL playoffs.
The Steelers themselves took a giant step closer to post-season football, with their destiny in their own hands as they sit two wins clear of divisional rival Baltimore, who play later Sunday against New England.
"I'm going to enjoy this one, and we're going to turn on the Sunday night game and root for the Patriots," said Rodgers.
A dour first half was notable mainly for an incident involving Pittsburgh receiver DK Metcalf, who reached into the stands and appeared to throw a punch at a Lions fan.
Though the Detroit supporter did not appear to be hurt, Metcalf may face disciplinary action.
Pittsburgh took a third-quarter lead with a two-point safety for sacking Goff in his own endzone, and never relinquished the advantage.
Steelers running back Kenneth Gainwell made one of the catches of the season, seizing the ball with one hand while horizontal on the floor before rising to sprint across the line for a touchdown.
With barely two minutes left, Steelers kicker Chris Boswell missed a 37-yard field goal that could have put the game almost beyond reach.
But the Lions could not quite capitalize, with an Amon-Ra St Brown catch and a Goff rush across the line both ruled out after extensive discussion among officials.
Jaguars respect?
Elsewhere on Sunday, a battle of two of the NFL's most in-form teams saw the league-leading Denver Broncos' 11-game win streak snapped by the Jacksonville Jaguars.
The impressive Jaguars won 34-20 for a sixth win in a row, breaking Denver's unbeaten home record this season, and moving to an 11-4 record.
Asked if Jacksonville - now dark horses for the number-one seed spot - would finally get respect from other teams, quarterback Trevor Lawrence joked: "Honestly, I hope not."
"Hope we don't get any. Everybody out there, just keep it up -- it's great."