United's run, which stretches back to a defeat at Liverpool in January 2020, saw them win 12 and draw seven of their games on the road this season.
Arsene Wenger's Invincibles also avoided defeat at home in 2003-04 as that Arsenal side became the first, and so far only, team to go through a full season unbeaten.
A makeshift United side ended their Premier League campaign on a high as 19-year old forward Anthony Elanga scored his first goal for the club in Sunday's win at Molineux.
Elanga fired United ahead in the 13th minute and Juan Mata netted a penalty in first-half stoppage time, giving United the win after wing-back Nelson Semedo had equalised with his maiden goal for Wolves.
With Champions League qualification secured and United bracing for Wednesday's Europa League final against Spanish side Villarreal, Solskjaer rested his regular starters as Elanga linked up with 18-year-old Amad Diallo in attack.
The Swedish youngster opened the scoring in his second start for United with a thumping header from eight metres after Daniel James picked him out with a fine cross from the left.
A flowing move allowed Semedo to draw level in the 39th minute, before Mata restored United's lead as he sent home keeper Rui Patricio the wrong way with a coolly taken penalty, given after a lengthy VAR check.
United stayed second on 74 points, 12 behind champions Manchester City, while Wolves finished 13th on 45 points, with their fans giving manager Nuno Espirito Santo a standing ovation after his last game in charge.
Espirito Santo is set to leave after four seasons in charge having guided the Midlands club back into the top flight in 2018 and then enjoyed two successive seventh-placed finishes.
The home fans gave Espirito Santo a standing ovation after the final whistle, with Wolves finishing 13th this term as they struggled to cope with injuries and the departure of some key players.
"I promised that I would stay strong but it was very special and very emotional," the Portuguese told BT Sport. "I will miss it. Now I want to rest."
Solskjaer praised his side's performance and for finishing the season with an unbeaten away record in the league but remained tight-lipped on whether United will offer 33-year-old midfielder Mata a new contract.
"Very happy, proud of them," he said. "They took the ball well, created chances and got the win they deserved. Very pleased for [Elanga] and he has a bright future ahead of him.
"Our home form hasn't been the greatest but what an achievement to go a season undefeated away.
"We are talking to Juan and it's a bit what he wants as well. I don't give him enough game time but he is such a professional and top quality. We will have a discussion."