(CNN) -- Manchester City manager Roberto Mancini insisted his team won't give up the English Premier League title without a fight as their 2-0 win over European champions Chelsea Sunday saw them keep their slim hopes alive.
Leaders and local rivals Manchester United had gone 15 points clear with a 2-0 win at bottom club Queens Park Rangers Saturday, but reigning champions City responded with a battling victory at the Etihad Stadium.
And a defiant Mancini still has hopes of reeling in United after goals from Yaya Toure and Carlos Tevez saw off Chelsea.
"We can't think that it's finished with 11 games to go. It's not my mentality or my players' mentality and we need to play like today. Both goals were fantastic," he told Sky Sports.
The game turned on an incident just after the break as Chelsea won a penalty when England goalkeeper Joe Hart brought down Demba Ba as he attempted to go round him.
Hart escaped either a yellow or red card for his infringement then rubbed salt into Chelsea's wounds by saving the resulting penalty from Frank Lampard, denying the midfielder his 200th goal for the Blues.
"I think Joe is the best keeper in England and one of the best in Europe," said Mancini.
City took the lead just after the hour mark as Toure received a fine pass from Spain star David Silva and scored with a low curling shot.
With five minutes left, Silva and Sergio Aguero exchanged passes for Argentine ace Tevez to convert from the edge of the penalty area.
The result has left City still 12 points adrift of United, while Chelsea have slipped up in the battle for Champions League spots and have just a two-point lead over fifth placed Arsenal.
In Sunday's other EPL match, Newcastle pulled six points clear of the relegation zone with an emphatic 4-2 win over fellow strugglers Southampton.
Meanwhile, the first major domestic trophy of the English season was claimed by Swansea as they beat minnows Bradford 5-0 in the final of the League Cup at Wembley Sunday.
Fourth flight Bradford knocked out Wigan, Arsenal and Aston Villa in a remarkable run to the final, but found Michael Laudrup's men a hurdle too far.
The writing was on the wall from the moment Nathan Dyer put Swansea ahead in the 16th minute after being played in by star striker Michu.
Spanish star Michu grabbed the second with five minutes remaining of the first half before Dyer scored his second goal just after the break after being set up by Wayne Routledge.
Bradford's sorry afternoon was complete when they had goalkeeper Matt Duke sent off for fouling Jonathan de Guzman, who got up to convert the penalty to make it 4-0.
De Guzman completed the rout with an injury time fifth as his side clinched a Europa League place for next season.