Hojlund, celebrating his 21st birthday on Sunday, became the youngest Red Devils player ever to score in four consecutive games for the club as he hit his fifth in his last six games to set Erik ten Hag's side on their way to a fourth victory from five matches across all competitions so far in 2024.
Garnacho's strike that deflected in off Nayef Aguerd less than a minute after a shocking miss from Emerson Palmieri at the other end proved a crucial moment for West Ham, who otherwise up until that point had delivered a lively attacking performance of their own just lacking in the final ball.
But their bright efforts waned considerably late on and Garnacho added a second six minutes from time after another costly mistake from Hammers new boy Kalvin Phillips was ruthlessly punished, the Manchester City loanee - at fault for Bournemouth's opener on his debut on Thursday - caught in possession in midfield by a combination of Scott McTominay and Hojlund before the former teed up Garnacho for a smart low finish arrowed into the far corner beyond Lukasz Fabianski, who had come on at half-time for the injured Alphonse Areola.
The success of United's youngsters was particularly poignant on a day when the club and fans remembered the legacy of the 'Busby Babes' and paid tribute to the victims of the Munich Air Disaster ahead of the 66th anniversary, which falls on Tuesday.
One particularly sour note for Manchester United though was the loss of Lisandro Martinez to another injury, the Argentine defender limping off after initially attempting to play through a knee problem sustained during a tussle with Vladimir Coufal in the second half.
Ten Hag's men jump up from eighth and leapfrog both Brighton and West Ham into sixth place in the Premier League table, with the Irons still winless in all competitions in this calendar year amid a worrying spell for David Moyes since their brilliant wins over Manchester United and Arsenal over the festive period.
Sunday represented West Ham's first league loss since they were thrashed by Wolves in early December, but a run of draws and shock FA Cup exit at Bristol City has dampened enthusiasm around the London Stadium.