Goals after the break from Winston Reid, Ricardo Vaz Te and Ravel Morrison condemned Andre Villas-Boas' side to its first home league defeat this season.
After a blank opening 45 minutes, Sam Allardyce's men struck three times in the space of 13 minutes to secure their first away win of the season, leaving Andre Villas-Boas' side three points behind Premier League leaders Arsenal.
It was the visitors who crafted the first chance of the game as Kevin Nolan headed wide from Downing's cross.
Allardyce's side frustrated Tottenham in the early going, with the hosts struggling to create clear-cut opportunities despite dictating the majority of the play.
It took more than 30 minutes for Spurs to finally exploit an opening in the West Ham defense, but Paulinho could only volley wide after latching onto a delivery from Andros Townsend on the right.
Townsend was at the heart of almost every Tottenham attack, and it was his ball in that should have provided the opening goal, but Jermain Defoe failed to get the telling touch with the goal at his mercy.
West Ham arguably created the best chance of the first half in the dying stages as Nolan lashed a volley across the face of goal following a clever Mark Noble free kick.
Tottenham made a rapid start to the second half, with Defoe denied twice by West Ham goalkeeper Jussi Jaaskelainen as they searched for the breakthrough.
West Ham came close to opening the scoring when James Tomkins' close-range header was clawed out by Tottenham goalkeeper Hugo Lloris, but the visitors did get the opening goal just after 66 minutes thanks to Reid.
The New Zealand international slotted West Ham's first away goal of the season from close range after his initial header from Downing's corner was blocked by Nolan.
And more misery was to come for Tottenham, as Vaz Te doubled West Ham's advantage just six minutes later. Noble set up the goal, sliding through a neat ball into the path of Vaz Te, and the Portuguese forward bundled home his second attempt following a fine save from Lloris.
Villas-Boas threw Roberto Soldado into the fray in an attempt to turn the game around, but West Ham put the tie beyond doubt after Morrison's superb solo goal.
The former Manchester United midfielder surged clear from inside his own half, beating Jan Vertonghen and Michael Dawson before lofting a composed finish into the back of the net.