As 0-0 matches go, this one at Old Trafford was not a bad spectacle, with United smacking the Chelsea wood work twice with De Gea producing a smart save from John Terry.
But Chelsea are still facing a serious relegation battle.
Guus Hiddink has overseen two draws since taking charge and would have hoped for a greater points return than this.
Chelsea are 14th in the Premier League but more importantly just three points away from the drop zone.
The Blues face high-flying Crystal Palace on Sunday at Selhurst Park and will hope to have Diego Costa, suspended for this outing, back in the side.
The Blues boss was forced into playing Eden Hazard up front on his own, as Loic Remy was out injured.
Three minutes in and ex-midfielder Juan Mata rattled Chelsea's crossbar from just inside the Chelsea penalty area with a venomous left-footer after good set- up play by Wayne Rooney.
However John Terry almost opened the scoring two minutes later when he bulleted a header from close range from a Willian corner. David De Gea produced a sensational tip over the save.
In a very positive start, United then had a phase of possession that almost saw Frenchman Morgan Schneiderlin arrow a smart right-footer, but the effort inched past Thibaut Courtois's left post.
Chelsea's post, Courtois's right, was rattled after a mazy run by Anthony Martial saw his shot crack it's base and zip along the goal line as United piled on the pressure.
Mikel picked up a yellow card for hauling down Martial after United produced a quick counter-attack on 28 minutes.
A blistering 30-yard strike by Rooney was acrobatically saved by Courtois, as the Belgium goalkeeper tipped the ball on the crossbar.
Referee Martin Atkinson, then produced a yellow card for an unlucky Schneiderlin on 29 minutes after he and Willian went 50/50 for a loose ball.
Chelsea restarted the second period like demons, with De Gea producing a double save two minutes in. Firstly from Pedro the second one from Oscar.
The game settled back to natural pace soon after but Untied should have scored 12 minutes in when Martial, the left sent in the perfect byline cross to Ander Herrera, whose first-time shot went straight to Courtois.
Quite how the Blues failed to score with 27 minutes s to go is unclear. Nemanja Matic raced clear on a breakaway, but when all he needed was to x.ip the ball over De Gea, he lost the plot, instead skiing the ball over the crossbar instead.
Chelsea's first replacement saw Willian replaced by Ramires on 70 minutes.
The tactic was one typical of Jose Mourinho and worked a teat as the blues snuffed out the final onslaught from the home side in the dying minutes.
Teams: Chelsea, Courtois, Ivanovic, Zouma, Oscar, Hazard, Mikel, Pedro, Matic, Willian, Terry, Azpilicueta
Subs, Begovic, Baba, Ramires, Traore, Djilobodji, Kenedy, Loftus-Cheek
Manchester United: De Gea, Mata, Martial, Rooney, Smalling, Blind, Young, Herrera, Schneiderlin, Schweinsteiger, Darmian
Subs, Jones, Memphis, Carrick, Romero, Fellaini, Borthwick-Jackson, Pereira
Referee, Martin Atkinson