Pascal Struijk thought he had snatched victory for the hosts when he struck from the penalty spot after 88 minutes but Danny Batth scrambled a last-gasp equaliser for the play-off hopefuls.
Daniel Farke's side had taken maximum points from their previous three festive fixtures, but lacked the spark needed to breach Rovers' well-drilled defence and were denied a 10th straight home win.
"It was definitely not our best game today. I think the lads looked a bit tired," he said.
"We feel a bit disappointed, yes. We know that we can't win all the games, the problem is you want to win them all. But if you can't, you take the point and move on."
Promotion rivals Burnley missed the chance to gain ground as they played out a 0-0 stalemate with Stoke City at Turf Moor.
Wilson Isidor fired fourth-placed Sunderland right back into the race for automatic promotion after a hard-fought 2-1 victory over third-placed Sheffield United.
The on-loan Zenit St Petersburg frontman's 35th-minute strike - his seventh goal of the season - proved decisive for the Black Cats at the Stadium of Light after Luke O'Nien's own goal had cancelled out Eliezer Mayenda's opener.
Elsewhere, substitute Alex Gilbert's added-time strike lifted Middlesbrough to a hard-fought 1-0 victory at Hull City.
Just as the visitors appeared on course for a fourth consecutive draw, Gilbert struck to lift Michael Carrick's side up to fifth and return the Tigers to the relegation zone.
Josh Windass scored from inside his own half in Sheffield Wednesday's 4-2 defeat of Derby County, Norwich City won 1-0 at Luton Town and West Bromwich Albion ran out 3-1 victors over Preston North End.
Bottom side Plymouth Argyle grabbed a last-gasp equaliser to draw 2-2 with Bristol City in their first match since the departure of Wayne Rooney as manager.
Fellow strugglers Portsmouth made a flying start to the new year with an emphatic 4-0 home win over Swansea City and Cardiff City held on for a 1-1 draw against Coventry City after the sending off of Callum Robinson. The Bluebirds had led early through Socceroo Alex Robertson.
QPR saw off Watford 3-1 to continue their recent revival, while Oxford United won 1-0 win at Millwall.
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