Carrick went with solidity for his first Premier League team selection after United’s recent maulings by Leicester City, Liverpool, Manchester City and – finally for Solskjaer – Watford.
He bolstered midfield by utilising Fred, Scott McTominay and Nemanja Matic to hold Chelsea at bay and, while David de Gea was busy in the first half, there was never a feeling of siege as United dug deep to come away with a point.
The big call was keeping Ronaldo on the bench. He was introduced in the 64th minute with United leading 1-0, but had minimal impact and was straight off down the tunnel when the final whistle sounded.
United at least showed the determination and resilience that had so often been glaringly absent in the dying embers of Solskjaer’s reign although there was very little attacking intent or quality apart from the great composure shown by Sancho for his second successive goal.
It will do him the world of good as he seeks to establish himself following his £73m summer move from Borussia Dortmund.
As for Carrick, if this is his final game in charge before Rangnick comes to Old Trafford, he can be well satisfied with his brief stint at the helm, winning against Villarreal in the Champions League and getting a share of the spoils here against a Chelsea side who have looked increasingly formidable in recent weeks.
It is a platform of sorts for Rangnick to begin his work and United will hope to continue their recovery against Arsenal at Old Trafford on Thursday.
Rudiger summed up Chelsea’s disappointment as he slumped to the turf at the final whistle knowing he could have been the match-winner.
The German defender saw a thunderous shot touched on to the crossbar by De Gea in the first half, but the big opportunity came with virtually the last kick of the game. He was unmarked at the far post to meet Christian Pulisic’s cross but took the instant volley and lashed his finish high over the top.
Manager Thomas Tuchel was equally agonised as he will know Chelsea did not take advantage of their overwhelming domination in parts of a game where they had 24 attempts on goal compared to United’s three.
Chelsea’s work was too hurried as they chased the winner although they were also frustrated by a United defence without suspended captain Harry Maguire.
Timo Werner is still too wayward, sending a very presentable chance well wide in the second half, but at least they have Romelu Lukaku fit again and Pulisic looked a lively threat when he came on.
This, in some ways, resembled many of Chelsea’s performances last season when they were superior, but never made the most of that advantage. Tuchel will certainly feel his side let United off the hook.
The Blues remain top but in what looks like it will be a tight title race between Tuchel’s side, Manchester City and Liverpool, they will regard this as two points dropped.