Dawson's own goal was his second in the Premier League
Manchester United needed a Craig Dawson own goal to overcome West Ham and strengthen their grip on a Champions League place.
On loan from Watford, Dawson has been outstanding in the Hammers' push for a top-four slot but settled the contest in the wrong way at the start of the second half as he turned Bruno Fernandes' corner into his own net under pressure from Scott McTominay at the near post.
Marcus Rashford and Mason Greenwood also went close in a one-sided contest as West Ham failed to threaten until Said Benrahma's introduction after an hour.
When the visitors finally pushed forward, Luke Shaw got in the way of Tomas Soucek's goalbound shot as United kept a fourth successive clean sheet for the first time under Ole Gunnar Solskjaer.
The result kept United in second but with the teams from fourth to seventh all failing to win this weekend, they now have a nine-point advantage over West Ham, who remain fifth, but do have a match in hand.
Cavini and Martial set to return for Man Utd in MilanReaction to Manchester United's win over West Ham
Solskjaer's men get the job done
Solskjaer will have been relieved to get the victory after conceding injury-time equalisers against Everton and AC Milan at Old Trafford in recent weeks.
It was not the greatest performance and United's first-half frustrations were summed up when skipper Harry Maguire bellowed an instruction to his team-mates that they needed to "liven up" and "stop giving the ball away".
With David Moyes setting up his side with wing-backs and three holding midfielders, West Ham provided a puzzle United struggled to solve.
Aside from Rashford glancing a header wide and Greenwood having an effort tipped on to a post and out for a corner by Lukasz Fabianski, United's passing lacked both the accuracy and crispness to move the visitors out of their containment structure.
In addition, as Rashford kept pulling wide and Fernandes tended to drop deep, neither McTominay nor Fred made runs into the box that might have allowed them to threaten the visitors' goal.
United were better after the break and Fabianski produced another excellent low save to deny Fernandes before Greenwood struck a post with a powerful shot at the end of a burst into the box.
David Moyes' West Ham are three points off a place in the top four
Moyes' wait for Old Trafford win continues
The result means Moyes remains without a win as an away manager at Old Trafford, a sequence that now extends to 11 defeats in 15 attempts in all competitions.
It is now 17 games since West Ham last beat Manchester United away from home, going right the way back to the famous Carlos Tevez winner that kept the Hammers up in 2007.
The win marks the first time United have done double over the Londoners since 2013-14, when Moyes took over from Sir Alex Ferguson.
West Ham never really looked capable of winning the game. The absence of Pablo Fornals through injury cost them an element of creativity they did not introduce until Benrahma came on, while Maguire and Victor Lindelof were assured on the rare occasions West Ham had a chance to create any aerial problems.
Moyes 'upset' with West Ham defeat
Shot-shy West Ham – the stats
Manchester United have only lost one of their past 23 Premier League games (W14 D8), after suffering three defeats in their opening six games of the season.West Ham have lost 50% of their 12 Premier League games this season against sides starting the day above them in the league (W4, D2, L6), compared to just 7% of their other 15 matches (W10, D4, L1).Manchester United have kept four straight clean sheets in the Premier League for the first time under Ole Gunnar Solskjær, last doing so in January 2018 when Jose Mourinho was at the helm.Only Leicester (4) have benefited from more own goals in the Premier League in 2020-21 than Manchester United (3, same as Liverpool), with Lewis Dunk and Jan Bednarek the other two players to do so against the Red Devils this season, alongside Craig Dawson.Only Harry Redknapp (15) has managed more away Premier League games at Old Trafford without winning than West Ham boss David Moyes (D4, L10), with this defeat his 14th such trip in the top flight (11 with Everton, 1 with Sunderland, 2 with West Ham).West Ham failed to manage a single shot on target despite seven attempts, the highest number of shots the Hammers have had in a Premier League game without any hitting the target since August 2013 vs Stoke City (9 shots).
Manchester United's next game is against AC Milan at the San Siro on Thursday, 18 March (20:00 GMT) in the second leg of their Europa League last-16 tie. Then they visit Leicester in the FA Cup sixth round on Sunday, 21 March (17:00).
West Ham's next game is a Premier League derby against Arsenal at London Stadium, also on 21 March (15:00).
Player of the match
with an average of 7.27Man UtdManchester UnitedManchester UnitedWest HamWest Ham UnitedWest Ham United
West Ham United
Line-upsMatch StatsLive Text
26Henderson29Wan-Bissaka2Lindelöf5Maguire23Shaw39McTominay17Fred21James18Bruno Fernandes10Rashford11Greenwood26Henderson29Wan-BissakaBooked at 35mins2Lindelöf5Maguire23Shaw39McTominayBooked at 49mins17Fred21JamesBooked at 90mins18Bruno Fernandes10RashfordBooked at 76mins11Greenwood
1Fabianski23Diop15Dawson3Cresswell41Rice5Coufal16Noble28Soucek31Johnson20Bowen30Antonio1Fabianski23Diop15Dawson3Cresswell41Rice5Coufal16NobleSubstituted forLanziniat 62'minutes28Soucek31JohnsonSubstituted forBenrahmaat 62'minutes20Bowen30Antonio
Home TeamMan UtdAway TeamWest HamPossessionHome62%Away38%ShotsHome15Away7Shots on TargetHome4Away0CornersHome6Away3FoulsHome12Away2
Match ends, Manchester United 1, West Ham United 0.