All the focus pre-match was on the young goalkeeper following his error in the reverse fixture two weeks ago and the Belgian will no doubt be the talk of the town once again after this one.
Benfica largely held their own in the first half and almost took a shock early lead when Chris Smalling guided a corner from the right towards his own goal but David De Gea was alert to make the save.
Svilar showed good alertness just afterwards to race out and deny Jesse Lingard as he raced clear as he looked to exorcise his demons from the previous meeting between the sides.
Anthony Martial was United’s star man for long periods, skipping past players with ease, but he could only fire a free kick from range over the bar after one such raid was halted prematurely.
Benfica responded in kind as Andreas Samaris fizzed an effort from range wide as the visitors continued to go toe-to-toe with United.
Martial’s directness was rewarded with just 14 minutes on the clock as he was brought down in the box by Douglas after some fantastic footwork down the left to give United a penalty.
The Frenchman assumed the responsibility from the spot but Svilar made a fine save low to his right to maintain parity.
Not to be outdone, De Gea made an equally as impressive save just three minutes later. Diogo Goncalves cut in from the left and took aim from range with an effort that looked destined for the top corner but the Spaniard flung himself to his left to make a stunning stop.
Martial might have had a chance at redemption after 24 minutes when Juan Mata was felled in the area but the referee waved away the protests on that occasion.
Romelu Lukaku grew into the game as the first half went on, first testing Svilar after cutting in from the right before heading over a Martial cross from the left from six yards when he really ought to have done better.
Martial and Lukaku combined once again as half-time approached with the latter feeding the former to fire over from the left channel.
United managed to make the breakthrough with just seconds to go before the half-time whistle and it came in cruel circumstances. Nemanja Matic strode forward from midfield and took aim from range. His low effort crashed back off the post, only to strike the helpless Svilar on the back and roll into the net.
The young Belgian had played excellently until that point but showed terrific mental strength almost immediately from the restart as he stayed big to deny Lukaku after the former Everton man streaked clear.
United went into the break with the lead but it was the visitors who started the second half better, albeit without truly threatening United in the early knockings of the half.
The Portuguese side had most of the ball in the opening exchanges of the half but they were limited to efforts from range, with Raul Jimenez forcing De Gea to make a save with a drive from range before Goncalves burst forward and forced the Spaniard into another stop at full stretch down to his right.
Benfica's best chance though was handed to them as Eric Bailly passed the ball straight to Jimenez on the edge of the United box but he could only hit the post with the help of a touch off Smalling.
Svilar made another good save to deny Lukaku after 71 minutes but was left cursing his defence three minutes later as they conceded yet another penalty. Samaris was adjudged to have brought down substitute Marcus Rashford after a great burst down the left from the birthday boy and Daley Blind stepped up to power the ball straight down the middle to double United’s lead.
From that point the game was over as a contest, with United’s victory meaning that they maintain their 100% record in the competition and all but secure their place in the last 16.