A first-half goal by Diogo Dalot and one each from Marcus Rashford and Ronaldo in the second set up a straightforward win for Erik ten Hag's side, who solidified their spot in the knockouts but still face a potentially challenging road to reach the Europa League last-16.
The hosts peppered the net of their Moldovan opposition, with Ronaldo going closest before 30 minutes from a weighted header back across the front of the goalmouth that was somehow kept out.
A deserved opener arrived just before the break when Dalot rose above the Sheriff defence and sent a bullet header past Maksym Koval, who dealt with five shots on frame out of a total of 13 by United in the opening half.
Defender Harry Maguire came on for the second half having missed the previous eight games with a hamstring injury.
Ronaldo, who was not in the squad for Saturday's 1-1 draw against Chelsea due to disciplinary reasons, heard roars of support from the Old Trafford faithful early in the second half despite sending a wide-open shot from the top of the area well over the goal.
The Man United No. 7 had the ball in the back of the net soon after, but the linesman's flag was up for offside and Ronaldo reacted by punting the ball into the stands in frustration.
A lovely ball in from Luke Shaw and an even better header from Rashford gave United their second, doubling the lead to Ten Hag's delight on the touchline and effectively killing off the game with an overmatched Sheriff.
Ronaldo did wind up on the scoresheet, smashing the rebound saved from his own header into the back of the net and then pointing triumphantly to the crowd in celebration.
With Group E leaders Real Sociedad also winning, second-placed United are likely to have to win a playoff round match against one of the Champions League third-place finishers, which already includes European heavyweights Juventus, Barcelona and Atletico Madrid, to get into the round of 16.