They may be taking the Champions League by storm, but Spurs face a real battle to qualify for next year's competition after extending their winless run in the league to four games on Tuesday night.
Van der Vaart looked to have come to Spurs' rescue when he kept up his remarkable record of scoring in every home appearance since joining the club.
But a horrible mix-up between William Gallas and Younes Kaboul gifted the visitors an immediate equaliser, Gyan taking full advantage with his third goal in two games.
Tottenham have now taken just two points from a possible 12 and are four adrift of the top four, all of whom have a game in hand.
Tonight's game kicked off a week after Spurs' historic Champions League win over Inter Milan.
But the home side's European exploits had taken a toll on their league form and they started the match only separated from Sunderland in the table by goals scored.
They started in determined fashion with Luka Modric's low strike forcing a fingertip save in the third minute from Craig Gordon, who was making his first appearance of the season after recovering from a broken arm.
Other long-range efforts from both sides were less successful before the recalled Kieran Richardson almost saw his shot deflect in off Kaboul.
There was a lack of a cutting edge at each end until Tom Huddlestone hit the crossbar with a nonchalant 30-yard effort.
That came in the 18th minute and was immediately followed by Anton Ferdinand, one of six changes for the visitors, limping off to be replaced by Phil Bardsley.
The crossing continued to disappoint, with even Gareth Bale failing to deliver anywhere near the kind of quality that saw him shoot to worldwide fame against Inter Milan.
Van der Vaart, who had recovered from a hamstring strain to start, did his best to provide it, playing a one-two with Huddlestone and firing a near-post shot which was easily saved by Gordon.
The goalkeeper then tipped over an ambitious David Bentley free-kick from wide on the left, while Gyan did well to direct a header on target from Boudewijn Zenden's cross.
A disappointing half looked destined to end goalless as Bentley, starting a league game for the first time in more than six months, unleashed a brilliant left-foot strike which Gordon did well to turn behind.
Half-time saw both sides make changes, Spurs withdrawing Roman Pavlyuchenko for Peter Crouch and Sunderland bringing off Cristian Riveros for Danny Welbeck.
But it was van der Vaart who should have broken the deadlock in the 52nd minute, the unmarked midfielder nodding Alan Hutton's cross wide.
That was immediately followed by the game's first real talking point, with Bentley going down in the box under a challenge from Zenden.
Referee Howard Webb booked Bentley for diving, and although television replays proved inconclusive, the home fans were furious.
They almost had something to cheer about when Van der Vaart found the target with his latest header, only to see Gordon claw it behind.
Bale blew a great chance to play Van der Vaart clean through just past the hour mark but made amends in the 64th minute by helping set up what has become a trademark goal from the Dutchman.
The winger's cross found Crouch at the back post and the substitute's header landed at the feet of van der Vaart to turn and fire home.
Spurs had not kept a clean sheet in the league since the opening day and they gifted the visitors an equaliser three minutes later, Gallas and Kaboul getting in each other's way and allowing Gyan all the time he needed to slide the ball beyond Heurelho Gomes.
There was a major flashpoint moments later when Lee Cattermole left Modric on the floor with a studs-first challenge that did connect with the ball before catching the Croatian.
A mass shoving match ensued before Webb produced the game's second yellow card.
The visitors ran down the clock by replacing Richardson with Steed Malbranque and the new man made an instant impact, with Gomes booked for tripping the midfielder just outside the box when a red card might have been shown.
The visitors finished the stronger and only more desperate defending prevented them snatching a surprise win.