The midfielder was recalled to the starting line-up for the first time since March as Jose Mourinho made eight changes. The following weekend, it's the FA Cup final at Wembley.
Mourinho is a serial victor.
Paul Pogba headed wide as the half wore on without any real drama, Moyes turning to Andy Carroll with 25 minutes remaining after the pair buried the hatchet following a falling out in the aftermath of the defeat to Manchester City.
"We are the second best team in the Premier League, a fantastic competition with lots of good teams with six teams trying to finish first", Mourinho told BBC Sport.
"We came second. I am not totally happy, that is not my nature. When it is not possible to be champion, second position is the best position available which is what we got".
"I am not critical of the performance at all". He said of some players on his roster, without naming names, "I don't believe they are going to make it".
Rafael Nadal breaks John McEnroe set record
In the quarter-finals, Lajovic will meet South Africa's Kevin Anderson who overcame German Philipp Kohlschreiber 6-3 7-6 (7). Two more sets and he would eclipse John McEnroe's record of 49 straight sets on any one surface.
In United's first game since legendary former manager Alex Ferguson had to have emergency surgery on a brain haemorrhage, the visiting fans showed their support to the 76-year-old Scot with persist chants of "we all love Alex Ferguson".
Jose Mourinho's men, beaten 1-0 at Brighton and Hove Albion on Friday, knew a point at London Stadium would be enough to ensure they will end the season as runners-up to rivals Manchester City.
While both players earned yellow cards from official Jon Moss, Mourinho had a different view of the incident.
When it comes to the narrative that has dominated much of Manchester United's season, Mourinho vs Paul Pogba, there are two sides of the argument, both with solid points.
Youngster Scott McTominay could play a role having impressed again against the Hammers on a night with few positives.
The Red Devils have kept more clean sheets than any other Premier League side this season (18).
"It's a big achievement for us". "It has been a tough job but a really good job".