After making their first appearances from the bench against Los Angeles Galaxy on Saturday, both Lukaku and Victor Lindelof were given their first starts against RSL in Utah, and it was £75m man Lukaku who had the first opportunity on goal as he fired wide after cutting onto his left foot.
Moments later, young midfielder Scott McTominay was denied by an excellent save by Nick Rimando, but it was not long before the home side began to make their mark with Joao Plata providing a constant threat.
After testing Joel Pereira, he was only denied a goal by superb defending from Jesse Lingard but Real Salt Lake got their reward when Silva ran onto a pass from Jefferson Savarino and slotted the ball past the goalkeeper.
Jose Mourinho was visibly frustrated on the touchline but his side soon improved and after Lukaku warmed the hands of Rimando from distance, they equalised through a fine effort from Mkhitaryan who found the back of the net from 20 yards after being provided with the opportunity by Lingard and Lukaku.
The home side - who are currently third from bottom in the Western Conference - made mass changes after the half-hour mark and the alterations did them no favours as United began to seize control of the fixture.
With seven minutes to go before the break, Lukaku got on the scoresheet for the first time in a United shirt after picking up a pass from Mkhitaryan and tapping into an empty net after rounding Rimando.
At half time, Mourinho opted to make 11 changes and that saw the likes of Eric Bailly, Ander Herrera and Marcus Rashford all introduced into the action but it led to the tempo of the game dropping significantly.
The biggest talking point ahead of the hour mark was a knock picked up by Mata, who needed to be replaced for Demetri Mitchell, but the tension to proceedings was instigated by meaty challenges from Herrera and Andreas Pereira.
Chances at either end were becoming a rarity but a talking point emerged midway through the second half when Valencia was sent off for what was deemed a dangerous challenge on Saucedo.
Mourinho was not happy and his frustration nearly turned to anger when Preston-born Luke Mulholland was provided with an opportunity to equalise from 15 yards out, but his shot went wide of Sergio Romero's post.
Soon afterwards, Chris Smalling should have made sure of the victory for United when Pereira found him six yards from goal, but he somehow directed his header off target.
Martial also wasted a good chance during the closing stages but despite failing to make the most of that opening, United were content with a hard-fought win ahead of their meeting with Manchester City later this week.