It all happened in injury time as goalkeeper Carroll raced out of his area with United desperately chasing a goal.
He made a bit of a hash of his clearance up the left touchline and it arrived at Mendes' feet some 50 yards from goal. He tried his luck, Carroll raced back, made it, but then spilled the ball clearly over the goalline - unfortunately the linesman wasn't in place to award the goal and a famous win was denied.
Nevertheless, it was another fantastic defensive performance on our travels - Ledley King and Paul Robinson were inspired - and a rare point at Old Trafford following seven straight defeats at the Theatre of Dreams.
The draw took our unbeaten run to eight matches with six wins and maintained our position in seventh in the Barclays Premiership.
With Jermain Defoe and Fredi Kanoute missing, Robbie Keane led the line himself in a 4-5-1 system with Dean Marney, Reto Ziegler and the returning Rohan Ricketts all supporting as best they could. Mendes and Michael Carrick sat deeper.
United, without Ruud van Nistelrooy, Luis Saha and the suspended Wayne Rooney, were the same with Alan Smith up front supported by Ryan Giggs, Paul Scholes, Darren Fletcher and Roy Keane.
There were a couple of scares in the first half and Paul Robinson was forced into action twice but United didn't really get on top.
We had the first efforts of the night via Marney and Robbie Keane but United started to get on top and Robinson had to scramble low to his left to fingertip wide Giggs' close-range prod after 13 minutes.
Cristiano Ronaldo headed the resulting corner just over but it took another 15 minutes for the next effort of note, Roy Keane volleying just wide from 25 yards.
Robinson's next stop arrived after 37 minutes as he blocked well with his feet as Smith sniffed out an effort from 16 yards. Then a blow for United as Giggs limped off, replaced by David Bellion.
Our best effort came in the final minute of the half as Carroll made a hash of Ziegler's cross, Keane fed the ball back to Mendes and the midfielder curled the ball onto the roof of the net with the keeper racing back into position.
United stepped up a gear at the start of the second half. Robinson did well to keep out Bellion one-on-one, Ronaldo lashed one wide and then Noe Pamarot steered Bellion's cross onto the post with King alert to beat Smith to the loose ball.
Robbie Keane had little to go up up front but we continued to plug away with the youthful spirit of Marney and Ziegler contagious.
We enjoyed some decent possession midway through the half but still it was United who carried the goal threat - Robinson this time saving at his near post from Bellion.
The last few minutes were fraught to say the least. Robinson was behind Miller's volley, King blocked again and then, incredibly, the 'goal' that wasn't at the other end.
As we came to terms with that moment, Robinson produced his best save of the match in injury time - clawing out Heinze's free-kick at full stretch and then watching helpless as Ferdinand banged the rebound into the stand.
GUIDE TO THE ACTION
2mins: Speculative volley by Marney from 25 yards curled wide of the target.
6mins: Smith, sliding in, inches away from Giggs' cross.
9mins: Giggs in at near post but lifted Heinze's cross over.
10mins: Ferdinand half-cleared Mendes pass to Keane, Keane spun and hit loose ball, Carroll made scrambling save.
11mins: Couple of vital interceptions, Naybet to block Ronaldo pass to Giggs then Carrick to keep out Giggs' pass to Scholes.
13mins: SAVE. Robinson fingertips to keep out Giggs' prod from close range.
13mins: CLOSE. From corner, Ronaldo climbed high to meet Giggs' inswinging kick but couldn't keep header on target.
28mins: CLOSE. Keane, joining in play, onto Naybet's clearing header and volleyed just wide from 25 yards.
34mins: Scholes whipped in cross to near post, Carrick flicked header just over own crossbar.
37mins: SAVE. Scholes worked ball through to Smith, central, 16 yards out, side-foot effort blocked by Robinson's feet.
37mins: SUB. Bellion for Giggs.
44mins: CLOSE. Carroll spilled Ziegler's cross, Keane picked up loose ball, laid it back to Mendes whose attempted curler from 22 yards landed on roof of net.
Half-time: United 0, Spurs 0
47mins: Regulation save but good hands from Robinson to hold onto tricky low shot from Ronaldo.
48mins: SAVE. Bellion onto Scholes' pass, good control, into box, Robinson out quickly to block the one-on-one.
49mins: YELLOW. Pamarot for foul on Heinze.
57mins: Ronaldo fired wide from 25 yards. More pressure from home side at start of second half.
59mins: WOODWORK/TACKLE: Bellion to byline, cross prodded onto his own post by Pamarot, Smith looked favourite to tuck away rebound but King made fine block.
60mins: Smith looping header from Heinze free-kick gathered easily by Robinson.
61mins: YELLOW. Marney for foul on Scholes.
62mins: YELLOW. Neville for foul on Ziegler.
74mins: We've enjoyed decent spell of possession but United quick break, Bellion into box, tight angle, Robinson save at near post.
75mins: Scholes worked a yard in box but shot blocked by combination of King and Naybet.
76mins: SUB. Miller for Fletcher.
78mins: Scholes shot blocked by King, ball looped up thankfully into Robinson's hands.
81mins: Keane went in with Heinze for Carrick's deep cross, went down claiming an elbow in face, nothing given.
82mins: Smith onto loose ball in box, lashed over.
84mins: SUB. Spector for Ronaldo.
85mins: Miller half-chance, chested down and half-volleyed straight at Robinson from tight angle.
88mins: Scholes almost onto Smith's flick, blocked, Keane follow up also blocked by King.
89mins: GOAL? Carroll way out of box, poor clearance, Mendes tried his luck from fully 50 yards, Carroll chasing back dropped the ball. Looked over goalline from press box, linesman way behind play, nothing given.
89mins: SUB. Gardner for Ricketts.
Injury time: SAVE. Robinson superb at full length to claw out Heinze's feee-kick from the edge of the box, Ferdinand blasted rebound into stand.
Full-time: United 0, Spurs 0
Line-ups: Manchester United: Carroll, Phil Neville, Heinze, Ferdinand, Silvestre, Ronaldo (Spector, 84), Giggs (Bellion, 37), Keane, Scholes, Fletcher (Miller, 76), Smith Subs: Djemba-Djemba, Ricardo.
Spurs: (likely 4-5-1): Robinson; Pamarot, Naybet, King, Edman; Ziegler, Mendes, Carrick, Ricketts (Gardner, 89), Marney; Keane. Subs: Fulop, Bunjevcevic, Yeates, Ifil.
Referee: Mark Clattenburg.
A magnificent defensive effort against United - and we were controversially denied a late winner at Old Trafford when Roy Carroll dropped Pedro Mendes' long shot over his own goalline.