Ian Holloway had threatened to quit if fined for making 10 alterations for the midweek defeat at Aston Villa, and had recalled his main men on Saturday afternoon.
However, it was referee Kevin Friend who took centre stage when he denied the home side what looked two clear first-half penalties, with Avram Grant's men then unable to make the most of their opportunities as the Israeli again faced calls for his resignation at the final whistle.
West Ham had not won in the league since the end of September. However, it was a positive start by the Irons, as fit-again Mark Noble stabbed a 20-yard effort wide.
Frederic Piquionne, who scored a penalty in the 2-2 draw against West Brom here on Wednesday night, broke down the left and cut inside the box, but his shot was charged down before Daniel Gabbidon headed a corner over.
West Ham were forced into a change after 18 minutes when midfielder Kieron Dyer, just back from a hamstring problem, was replaced by Mexico winger Pablo Barrera.
Blackpool had a good spell, as DJ Campbell fired a snapshot straight at Robert Green.
West Ham had what looked a strong penalty claim turned down by referee Friend when left-back Stephen Crainey appeared to trip Barrera out on the right touchline.
At the other end, David Vaughan drove into the left side of the West Ham area before releasing a low shot which flew just wide of Green's post.
The home side were again screaming for a spot-kick when Victor Obinna's fierce 18-yard drive struck Craig Cathcart on the arm, but once more the referee was not interested.
Blackpool had to replace goalkeeper Matthew Gilks at the start of the second half, after he had appeared to jar his knee when clearing a goalkick, with Richard Kingson coming on for an unexpected second appearance of the week.
West Ham had another great chance when Luis Boa Morte was slipped into the left side of the penalty area by Scott Parker, but dragged his shot wide of the far post.
Blackpool captain Charlie Adam spotted Green off his line and so tried an audacious chip from just inside the West Ham half which, fortunately for the backpedalling keeper, dropped over the bar.
Obinna drilled the ball high and wide after it was cut back from the touchline - much to the frustration of the Irons fans behind the goal in the Bobby Moore Stand.
Blackpool substitute Marlon Harewood almost returned to haunt his former club, but his scrambled goal from a free-kick was ruled out for offside.
Parker scampered into the Blackpool box before cutting the ball back to Barrera on the penalty spot, but his sidefoot effort was blocked by Ian Evatt.
West Ham substitute Carlton Cole almost had an instant impact but his deflected close-range effort struck the outside of the post.
Gary Taylor-Fletcher then skied the ball over the bar when arriving in the penalty area following a quick Blackpool break down the left.
Kingson made an acrobatic one-handed save to tip Noble's curling 20-yard effort behind.
There was an almighty let-off for the hosts when Harewood somehow stabbed the ball wide from six yards before Green deflected away a goalbound effort from Cathcart.
In stoppage time, Benni McCarthy headed over as once again the Hammers were booed off by the disgruntled Upton Park faithful.