Bruno Fernandes and Marcus Rashford converted from the spot to extend Everton's winless run in the Premier League to 11 games.
Victory takes United to within eight points of fourth-placed Aston Villa and three of Tottenham in fifth.
Defeat leaves Everton still just five points above the relegation zone, having played two more games than 18th-placed Luton.
Back-to-back defeats to Fulham and Manchester City had dented a charge from Erik ten Hag's men towards the top four.
But with Villa and Tottenham facing off on Sunday, the Red Devils made the most of Everton's mistakes to close on their rivals for a return to the Champions League.
Alejandro Garnacho scored a goal of the season contender when the sides last met in November with a stunning overhead kick.
The Argentine was again the difference between the sides as it was his quick feet that twice provoked spot-kicks.
James Tarkowski was the first Everton defender lured into a mistimed challenge on 10 minutes and Fernandes rolled home his eighth goal of the season.
Scoring goals has been Everton's shortfall all season and it was a familiar tale for the Toffees.
A combination of Amadou Onana and Ben Godfrey should have opened the scoring just three minutes in.
Three times Dwight McNeil then tried his luck with his closest effort flashing inches wide.
And even when the visitors did hit the target, Andre Onana produced a flying save to deny James Garner.
Instead, they soon trailed by two due to another self-inflicted blow.
Garnacho danced through a series of challenges on the edge of the box before he was chopped down by Godfrey.
Just like he did at Goodison Park earlier in the season, Fernandes passed over penalty duties to Rashford.
Jordan Pickford was unable to deny his England international teammate as Rashford fired home his fifth goal in nine Premier League games.
Pickford did succeed in keeping the score down as he denied Fernandes a second from a well-struck free-kick and low drive that was arrowing towards the bottom corner.
Garnacho was also wasteful with a series of chances to add a goal to his involvement in the two penalties.
However, United were bailed out by Everton being even more toothless up front.
For the 16th time in 28 league games this season, United gave up 16 or more shots on their goal.
But Everton failed to make any of their 20 efforts count.
And they nearly conceded a third penalty in stoppage time when Rashford was wiped out by Jarrad Branthwaite, but the offside flag came to Everton's rescue.
