Cristiano Ronaldo scored his 17th goal of the season to earn Manchester United a point after David de Gea had frustrated Chelsea with several superb saves, leaving United fans happily surprised.
Ronaldo ran onto a ball over the Chelsea defense from Nemanja Matic and delivered a clinical finish in the 62nd minute, two minutes after Marcos Alonso gave the visitors the lead.
Reece James later curled a shot against the post for Chelsea, which dominated the first half but found United goalkeeper David de Gea in fine form, without whom United would very likely be in the bottom half of the EPL table.
"Not only the goal Cristiano scored but his whole performance, his attitude at the age of 37, this is not normal to do that," said Man United interim manager Rangnick.
"If he plays like he did today he can still be a big help to this team.
"It was a good point for us. In the first half Chelsea dominated the game. You can see that they have top players and are well organised, and it's not so easy to get hold of them," added Rangnick.
Chelsea had won their past eight games on the road in all competitions - and they will wonder how they failed to make it nine as this draw ended that club record run.
Taking their chances has been an issue throughout this season and although De Gea was in incredible form the Blues will no doubt feel frustrated they could not score more than once.
In the end, it was a missed opportunity for the visitors but one that shouldn't dent their chances of finishing in the top four, with seven points needed from their five remaining games to guarantee that.
With only three games left to play in the league, United stayed in sixth place - five points behind fourth-place Arsenal and having played two matches more than its rival for Champions League qualification.
