United boss Jose Mourinho made four changes to the team that started against Liverpool on Saturday afternoon. Victor Lindelof and Daley Blind replaced Matteo Darmian and Phil Jones at the back, while Juan Mata and Rashford came in for Anthony Martial and Ashley Young.
As for Benfica, a suspension for Andre Almeida saw 20-year-old Ruben Dias come into the home side's defence. The headline team news for Benfica saw 18-year-old Svilar become the youngest-ever goalkeeper to play in the Champions League, while their leading scorer Jonas was left on the bench.
The home side made a confident start to proceedings in Lisbon, with Eduardo Salvio leading a couple of dangerous counter-attacks as United took their time to settle.
It was Salvio that had the game's first half-chance in the 15th minute after meeting a low cross from Alex Grimaldo, but the attacker's effort was wide of the post as United escaped a dangerous situation.
Benfica continued to force the issue as the first period approached its mid-point, with Jimenez winning his fair share of aerial battles against Chris Smalling and Lindelof.
Jimenez fired one into the stands in the 30th minute as the hosts continued to look the most likely, although Rashford had a decent chance in the 32nd minute, with the England international heading a Blind cross over the crossbar.
Mkhitaryan had United's final chance of the first half after breaking away from the Benfica defence, but the Armenian fired over the crossbar as the two teams headed down the tunnel at 0-0.
Ander Herrera fired well wide of the post early in the second period after smart work from Rashford, before the latter tested the handling of Svilar with a powerful strike from distance in the 50th minute.
Matic whistled one over Svilar's goal on the hour as United continued to look the more likely, and the visitors finally made the breakthrough in the 64th minute when Benfica's teenage goalkeeper Svilar bizarrely carried a long-range Rashford free kick over the line after taking up a high starting position.
It was a tough moment for the Benfica goalkeeper, who had looked suspect from high balls into the penalty box.
Martial replaced Rashford 15 minutes from time after the teenager limped off the field, and the Frenchman brought a smart save from Svilar in the 79th minute as United looked for a second.
Dias volleyed over the United goal in the 84th minute as Benfica, who had their captain Luisao sent off late on, threatened, but Mourinho's side held on to secure another win as they moved onto nine points from three Group A fixtures.