Ronaldo sent Tim Krul in the wrong direction in the 75th minute after Max Aarons pulled the Portuguese to the ground on the edge of the six-yard area.
Until then, the Red Devils were hardly likely to attack, but Alex Telles hit the crossbar with a deflected free kick in the first half.
They also had David de Gea to thank for making two good stops against Teemu Pukki and Ozan Kabak as Norwich put on a spirited performance.
Victor Lindelof worried when he was pulled down in the second half while holding his chest, despite Rangnick saying the Swedish defender had taken tests and “appears to be okay”.
The win moves Manchester United to fifth ahead of Arsenal and Tottenham. Norwich remains at the bottom of the goal difference, three points for safety reasons.
Ronaldo saves United
After making a number of changes for the Champions League midweek draw with the Young Boys, Ralf Rangnick restored the XI, which Crystal Palace defeated in their first game last weekend.
But despite a full week of preparation, United looked sluggish and rarely threatened a team that has conceded more goals this season than any other in the Premier League.
Ronaldo had to wait until 38 minutes to get his first look on goal, running towards Scott McTominay’s pass before striking inside and rolling in a left-footed shot that was turned away by Krul.
United continued to lose in the second half but, like they did against Palace, managed to find a way, with Ronaldo emphatically taking the spot-on penalty after Aarons dragged him down in an attempt to hit a right flank.
De Gea maintained good form this season as well, surfacing in full force to tip a bubbly Pukki shot over the bar before blocking Kabak’s late header.
This means the Red Devils have cleared for the first time in a streak of four straight games from February to March 2021, and have won three straight league games for the second time this season.
There’s also a bit of history for Rangnick, who was the second Manchester United manager after Ernest Mangnall in 1903 to clean his first two responsible league games.
Injury, suspension and illness forced Norwich boss Dean Smith to make five changes to the team that lost at Tottenham last week, including a first start of the season for Przemyslaw Plachet and recalls for Kabak and Dimitrios Giannoulis – whose last start a 7-0 defeat at Chelsea in October.
In the 20th minute they suffered another injury when captain Grant Hanley had to leave the field with a shoulder injury. Midfielder Jacob Sorensen had to play alongside Kabak in the Canary Islands defense.
But despite the patched up character of the team, it was an effort full of effort and strain.
The lack of offense once again let them down – no team has scored fewer than Norwich’s eight Premier League goals this season – although they can rightly point to an impressive performance from De Gea.
There was also some good news on the injury front when Todd Cantwell left the bench in the second half for his second appearance since September.
Despite disappointment with the defeat, it was an achievement to build on as Smith prepares to welcome former Aston Villa club to Carrow Road next week.