Zenden's mistimed header sailed over Robert Green in what was the veteran midfielder's final match before quitting the Black Cats this summer.
Stephane Sessegnon's pinpoint 20-yard effort and Cristian Riveros' stoppage-time third sealed the victory in the second half, during which the Hammers fans demonstrated their gallows humour with more than one ironic conga.
Not even the introduction on the hour of Footballer of the Year Scott Parker could rouse the Hammers, whose team selection was a nod to next season, with a summer clear-out expected.
The game was also caretaker boss Kevin Keen's one chance to bid for the manager's position, although it was likely to be a forlorn one - regardless of today's result.
Sunderland were playing for prize money only but they played their part in a wide-open start to the game, Asamoah Gyan twice shooting straight at Robert Green, who also pouched a mishit Nedum Onuoha volley.
West Ham responded with a Frederic Piquionne air shot, while Simon Mignolet saved at the feet of Zavon Hines and palmed away a fine left-foot curler from Freddie Sears.
The Black Cats goalkeeper got away with spilling a Thomas Hitzlsperger free-kick, with Onuoha clearing the danger and also blocking James Tomkins' shot from the resulting corner.
The near misses failed to alter what was a suitably funereal atmosphere at Upton Park, something which did not improve when West Ham fell behind in the 17th minute.
The ball was played to Ahmed Elmohamady and his right-wing cross picked out the unmarked Zenden, who appeared to mistime his header, which nevertheless sailed over Green. It was Zenden's second goal in three games and came in the week he confirmed he would be leaving Sunderland.
The Hammers tried to respond but the visitors were looking a threat on the break and Sessegnon steered a 20-yard shot too close to Green.
The deathly silence was briefly broken as Parker warmed up along the touchline at Upton Park, where there were plenty of empty seats.
And with West Ham failing to test Mignolet until the stroke of half-time - when Hines' shot was blocked by the keeper - it appeared only a matter of time before the England midfielder was given the chance to say his farewells.
There was slightly more urgency about the home side at the start of the second half and Hines lured Phil Bardsley into a tackle that earned the defender a yellow card.
Jack Collison's free-kick failed to catch out Mignolet at the near post before a group of supporters in the Sir Trevor Brooking Stand started the first of the afternoon's ironic congas.
It was abruptly halted in the 51st minute when Sunderland doubled their lead, Sessegnon allowed to bear down on goal before striking a low 20-yard shot that clipped the post on its way past Green.
The Hammers made a double substitution, bringing on Lars Jacobsen and Victor Obinna for what were set to be their final appearances for the club.
Gyan drilled narrowly wide from the tightest of angles and Jack Colback's volley stung the palms of Green as the visitors tried to kill the game.
The pocket of fans that had gathered at the front of the Sir Trevor Brooking Stand attracted a cordon of stewards and police, although their behaviour remained harmless.
And the stadium was united in appreciation just past the hour mark as Parker made his entrance.
Steed Malbranque was booked for a foul on Obinna, who should have made him pay when he nodded the resulting free-kick straight at Mignolet, before a limping Bardsley was replaced by Riveros for the final quarter.
Gyan was replaced by Jordan Cook for the final 18 minutes, during which Jordan Henderson's deflected flick went close.
And it was Henderson who laid on a stoppage-time third, crossing for Riveros, who lad all the time in the world to Hammer home the final nail in West Ham's coffin.
A late equaliser for West Brom at St James' Park capped a good day on the road for the visitors - as they moved above their north-east rivals and into the top half of the table.