The USA striker finally broke United's resistance in the third and final minute of injury time to secure a well-deserved point in the snow at the Lane.
Clint had already been denied at point-blank range earlier in the second half by David De Gea in the United goal.
The Spanish goalkeeper also kept out Jermain Defoe, Aaron Lennon and Gareth Bale as we pinned the visitors back in search of an equaliser to Robin van Persie's header in the first half.
Only seconds remained when the outstanding Aaron Lennon squared for Clint to send the Lane crowd into raptures.
Asked how he felt at that point, Clint said: "It was relief. Anytime you can get a point when you are looking at defeat, it almost feels like a win. It was great."
The draw extended our current run to one defeat in 11 in the Premier League and means we've taken four points from the league leaders - United have won 18 of their 23 matches to top the table by five points. We remain in fourth place.
"We tried so hard to get the equaliser and it just seemed like it wasn’t going to be our night," added Clint.
"We knew getting crosses in was causing them problems and eventually we got one more cross in, the goalkeeper got a punch to it, the ball went to Aaron and he hit a cross, I just tried to keep it in the frame and I’m delighted it went in."
Clint could hardly believe it when De Gea managed to touch wide his point-blank effort in the 51st minute.
"It was a great ball in from Mousa and I got a good touch on it but it was under my feet a little, so I couldn’t hit it to the side," he explained.
"I tried to hit it hard and low, the keeper was leaning the other way but he made a great save.
"I was just thinking maybe it wasn’t going to be our day but we kept plugging away, kept getting shots on goal and in the end, we finally got what we deserved."