Liverpool almost scored through Dirk Kuyt with moments remaining but had to settle for a point that left it on 37 points, 10 fewer than Arsenal and eight behind Manchester United.
West Ham beat United 2-1 on Saturday to stop the Red Devils moving further ahead and instead let Arsenal move into first place with a 4-1 win at Everton.
That gave Liverpool hope of re-igniting its challenge for the title, but it was unable to take full advantage.
"The team was playing well and creating chances and normally you finish by winning,'' Liverpool manager Rafa Benitez said.
"They have a fantastic record, but we had our chances.
"Their keeper and the defenders were really good.''
With Daniel Agger and Sami Hyypia both missing because of injury, Benitez fielded Alvaro Arbeloa in central defense alongside Jamie Carragher.
The pair were relatively untroubled in the first half at Eastlands, with Liverpool having the best chances from long-range shots by Steven Gerrard and Yossi Benayoun.
Fernando Torres twice came close to scoring at the start of the second half, the second chance coming from a mistake by goalkeeper Joe Hart, while Benayoun had a shot from outside the area pushed over the bar by Hart.
With three minutes left, Kuyt almost forced the ball over the line from close range but it was cleared off the line and Benayoun had a shot on goal blocked and deflected wide by Dunne.
"It was just backs to the wall,'' Dunne said.
"We're at home and we want to win games at home, but you have to respect sides like Liverpool. It was a difficult game and we got the result.''
City, which is still unbeaten at home in the league, stayed a point behind fourth-place Liverpool, which is four behind Chelsea but with a game in hand.
"We want to progress up the table,'' said Benitez, who added that he hoped to sign "maybe one, maybe two'' players during the January transfer window.
Derby remain anchored
At the other end of the standings, Derby stayed firmly at the bottom when it lost 2-1 to visiting Blackburn.
The Rams, who have won just once since getting promoted to the Premier League by winning last season's playoffs, led in the 27th at Pride Park when Matt Oakley hit a shot from Tyrone Mears' cross under goalkeeper Brad Friedel.
Steve Howard missed a chance to make it 2-0 in the 36th when Friedel saved his penalty kick and Roque Santa Cruz, who had already had a goal ruled out because of a foul, equalized in the 39th with his eighth goal in five games.
The Paraguay striker scored from a rebound after goalkeeper Lewis Price had saved a shot by Benni McCarthy, and Blackburn led three minutes later when winger David Bentley hit a 25-metre shot.
While Blackburn's first win in five league games lifted it to ninth place, Derby remained last with just seven points from 20 matches, eight fewer than next-to-last Fulham.