Andre Ayew, Winston Reid, Michail Antonio, and Andy Carroll were all on target as West Ham compounded Swansea’s worries with a 4-1 win.
Fernando Llorente, on as a substitute, claimed a Swansea consolation two minutes from time with his fifth goal in six games, but even then Carroll had the final word.
The victory takes West Ham towards mid-table but these are dark times for Swansea and their American manager, who might not welcome 2017 in a job he was only appointed to in October.
Bradley admitted that his fate might rest on home games against West Ham and Bournemouth, on New Year’s Eve, but the Swansea fans had clearly made their minds up when Reid headed home four minutes into the second half.
“We want Bradley out,” reverberated around the Liberty Stadium as Swansea were consigned to the seventh defeat of the American’s 11-game reign.
Supporters also turned their anger on chairman Huw Jenkins, who had used his programme notes to defend the club’s summer takeover.
But, in the absence of their American owners, Swansea lost for the 12th time this season and are now four points from safety having conceded 28 goals under Bradley.
Swansea had the first chance when Jack Cork’s tenacity gave Borja Baston a glimpse of goal, which he chose to take rather than slip in the fast-supporting Gylfi Sigurdsson.
The ball drifted well wide and Borja must have regretted his choice when West Ham claimed the lead a minute later.
Carroll always enjoys seeing Swansea, having scored five goals and had three assists in his previous eight appearances against the Welsh club.
And the England striker claimed another assist when he pulled on to Angel Rangel in the right-back position and diverted Mark Noble’s centre across goal.
Cheikhou Kouyate’s presence bewitched Lukasz Fabianski at the near post as the goalkeeper fumbled the ball into the path of Andre Ayew for the softest of goals.
Ayew almost had another from Dimitri Payet’s cross and the anxiety in Swansea ranks was quickly spreading around a stadium with each poor home touch greeted by a chorus of groans.
Payet was allowed to cut inside onto his right foot to force a goal-line stop from Fabianski and it was only a final careless pass which prevented West Ham from doubling their advantage.
Swansea lacked the pace to profit from their own counters but Jay Fulton and Rangel worked space well to create a chance for Sigurdsson.
As if to sum up Swansea’s performance, the usually reliable Sigurdsson mishit his attempt so badly it went out for a West Ham throw.
Sigurdsson was more accurate from a 25-yard free-kick, which Darren Randolph pushed around a post, but the goalkeeper waved over a Cork header on the stroke of half-time.
Swansea sent on Llorente and Jefferson Montero to engineer a rescue act, but West Ham scored again within four minutes of the restart.
Payet sent his corner towards the six-yard box and Reid got between Alfie Mawson and Cork to head home his second goal of the season.
Swansea fans instantly vented their frustration at Bradley and Jenkins, but Randolph was called upon to stop Wayne Routledge and Sigurdsson before West Ham sewed up matters.
Fabianski pushed aside Edimilson Fernandes’ shot, but Havard Nordtveit followed up to drive the ball back into the area for Antonio to deflect home his eighth goal of the season.
Llorente raised some Swansea cheer from close range, but Carroll smashed home an angled volley moments later.