It was Sherwood who had given the hosts the lead shortly before half-time, whilst Don Hutchison levelled things midway through the second half. The visitors had missed a penalty before the scoring began, with England hitman Kevin Phillips way off target from the spot.
The only black spot for Spurs was the sending off of Ben Thatcher, who departed during injury-time in the second half.
The game got off to a ferocious start, with Les Ferdinand nearly puting Spurs into a the lead with a header which deflected off Jody Craddock and seemed to be past Thomas Sorensen, until the Dane stretched out an arm and kept the ball out.
Spurs continued their good start with Darren Anderton trying his luck from 30 yards, his effort maybe a yard out with his accuracy as the ball flashed past the post.
Sunderland's first attacking foray ended with the ball in the Spurs' net, but Hutchison was adjudged offside after taking Niall Quinn's header into his stride and hammering the ball past Neil Sullivan.
It was Hutchison who had the next chance, with Phillips drifting to the right wing and swinging in an inviting cross which the former Everton and Liverpool midfielder headed over the crossbar.
Sunderland, having weathered the initial Spurs start, could have taken the lead on the half hour, with Hutchison turning provider and curling a super cross which found Quinn unmarked at the far post, but his header went into the side-netting.
Immediately Spurs came back and Sorensen produced the save of the match by diving one-handed to his right to prevent Anderton giving the hosts the lead.
Lively
The game was proving lively, and in the 36th minute the visitors were awarded a penalty after Ramon Vega handled the ball from a Sunderland free-kick.
England international Phillips strode up and blasted the ball high and over the crossbar.
Almost immediately, Sergei Rebrov's flick on found an unmarked Ferdinand, whose rasping volley was brilliantly tipped over by Sorensen.
Spurs eventually broke the deadlock from a corner, Anderton's kick diverted inadvertently into the path of Sherwood who stabbed home the goal from maybe four yards in the 43rd minute. The second half was very tame until the 62nd minute, which saw a free-kick from the Sunderland left floated in and Hutchison rising to head the ball past a static Neil Sullivan.
From there on, both teams cancelled each other out until Armstrong's winner, which really came out of the blue.
There was still time for Thatcher to get himself sent off for two bookable offences, the second a case of clear dissent after failing to win a corner, and Steve Clemence miss a sitter from eight yards.
