Manchester City survived a second-half onslaught to prevent Liverpool ending 2007 with three league wins in a row.
Dunne and co somehow thwarted the likes of Torres
Fabio Aurelio came closest to scoring in a cagey first half, his long-range strike tipped over by City's Joe Hart.
Fernando Torres squandered two good chances and Hart palmed away a fierce effort from Yossi Benayoun as the Reds poured forward after the interval.
Dirk Kuyt had a glorious opportunity in the 87th minute but Hart and Richard Dunne combined to clear his header.
It meant Liverpool will go into the new year 10 points behind leaders Arsenal, with a game in hand.
Their previous clash against Manchester opposition, a 1-0 defeat by United, had finished with searching questions being asked about their title credentials.
This time they will be wondering how they failed to see off a City team that could not get close to the fluency they began the season with.
Liverpool manager Rafael Benitez again shuffled his pack, making five changes to the team that stole three points at Derby in their last outing.
And with the hosts in the middle of an uncertain spell, following two successive draws in the league and a Carling Cup exit, both teams struggled to establish any attacking rhythm early on.
Indeed, considering the talent and reputations on display, the first quarter was surprisingly bereft of genuine quality.
The first shot on target arrived after 25 minutes - a Harry Kewell strike collected by Hart at the second attempt - but it appeared to spark the game briefly into life.
A brave block from Jamie Carragher in the box denied City's subdued playmaker Elano a clear opening and Michael Ball deflected Kuyt's effort wide at the other end.
Reds defender Aurelio then twice came close to embarrassing Hart with two long-range strikes: the first bounced just past the post, while the second was helped over by the England Under-21 keeper's fingertips.
The game needed perking up and Liverpool did their best to break the deadlock with a flurry of chances in the opening 20 minutes of the second half.
Aurelio surged down the left and his cross fell at the feet of Torres, who shot tamely at Hart, with a fourth goal in three Premier League games beckoning.
Steven Gerrard then played the Spanish striker through after Stephen Ireland gave away possession, only for Torres' effort to roll wide after squirting through Hart's legs.
Although City were being roared on by the majority of a record Eastlands crowd all the action was taking place in their goalmouth.
Gerrard, who had gone close with a free-kick, strode through acres of space and the ball was worked through to Benayoun before the Israeli international unleashed a stinging drive that Hart palmed behind.
City boss Sven-Goran Eriksson replaced the off-colour Elano with Rolando Bianchi in a bid to ignite his team into action but his defensive players continued to be overworked.
Liverpool fans and Benitez were fuming when Dunne appeared to haul down Torres with the in-form forward in full flight.
Torres was then booked for a challenge on Micah Richards and the visitors' frustration was complete when the ball was worked back into the box after an Aurelio corner.
With the goal gaping, Kuyt failed to get enough power on his header, Hart clawed it away and Dunne hacked away from under the bar.
Manchester City manager Sven-Goran Eriksson:
"I think we defended very well. It was a good game but there were not a lot of chances.
"I am happy with one point and happy with a clean sheet, which is good against Liverpool.
"We're not disappointed. When you play like we did against a team like Liverpool, you can't be disappointed. But I'm not 100% happy, because we wanted to win the game."
Liverpool boss Rafael Benitez:
"We're a bit frustrated. We had a lot of chances, played well and had lots of possession. I'm pleased with the team but disappointed with the result.
"We had enough chances to win against a good team who are difficult to beat at home, and the commitment of all the players was fantastic.
"A clean sheet when you are playing away from home is a good thing but after 17 attempts on goal, you think you must win."
Man City: Hart, Onuoha, Richards, Dunne, Ball, Ireland (Gelson 61), Hamann, Corluka, Petrov, Elano (Bianchi 70), Vassell (Geovanni 74).
Subs Not Used: Isaksson, Garrido.
Liverpool: Reina, Finnan, Carragher, Arbeloa, Aurelio, Benayoun, Gerrard, Mascherano, Kewell (Babel 74), Torres, Kuyt.
Subs Not Used: Itandje, Riise, Voronin, Alonso.
Ref: Uriah Rennie (S Yorkshire).
BBC Sport Player Rater man of the match: Manchester City's Richard Dunne 6.91 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.