Jeff Schlupp gave Palace some hope after Casemiro’s sending off but Erik ten Hag’s side held on to claim another win.
The result sees United claim a fourth consecutive victory since their last-minute defeat at Arsenal last month.
The hosts were awarded a penalty after five minutes when VAR adjudged Will Hughes to have handled Rashford’s cross inside the box.
Fernandes stepped up to score from the spot kick and United dominated the first half but failed to score another goal.
United doubled their lead after the break when Luke Shaw set up Rashford who produced a fine finish.
The game turned after 70 minutes when Casemiro was sent off following a VAR check for grabbing Hughes’ neck.
Five minutes later, Palace grabbed a goal back as Schlupp diverted past David de Gea from a corner.
The visitors poured forward looking for an equaliser but Ten Hag stemmed the tide by sending on Harry Maguire, loan signing Marcel Sabitzer and Victor Lindelof, who replaced fellow substitute Alejandro Garnacho,as they held on to win.
“The first 70 minutes was all ours, we dominated the game and we played really well, A big compliment for the team, a lot of energy and they played really well in possession and in the defence transition,” Ten Hag said in a TV interview.
“The last 20 minutes we showed we can battle, we can fight. It’s a big team spirit, they stand [up] for each other and we are happy with that,” he added.
Information from Reuters was also used in this report.