Charlie Adam scored from the penalty spot after Baggies defender Pablo Ibanez was harshly sent off as the last man after just 11 minutes.
The away side's task became even harder when Gonzalo Jara also saw red after 29 minutes, following a ludicrous two-footed challenge on Luke Varney, who scored his side's second on the hour mark.
It proved the decisive strike as Youssouf Mulumbu pulled a goal back and set up a nervy final five minutes during which Paul Scharner and Steven Reid both almost nicked what would have been a barely believable point for the visitors.
In the end Blackpool did enough to claim their first home win in four games and end the Baggies' six-game unbeaten league run.
West Brom gave first league start to Simon Cox while Jara joined him in place of injured duo Jonas Olsson and James Morrison.
Cox almost gave his side an early lead following a neat exchange with Chris Brunt before his low shot was tipped wide by Matt Gilks.
But the Baggies' hopes were dealt their first major blow as they lost their first of two players to a red card after 11 minutes, albeit in contentious circumstances.
DJ Campbell ran onto an Adam throughball and with only Ibanez in attendance he went down a little easily under the merest of contact from the defender.
Despite that referee Michael Oliver, who at 25 became the Premier League's youngest ever match official earlier this season, had no hesitation in pointing to the spot and then showing the obligatory red card to Ibanez as the last man.
Adam blasted the penalty passed Scott Carson, who did get hands on the ball, to give his side the lead.
West Brom boss Roberto Di Matteo shuffled his reduced line-up by replacing Cox with Steven Reid, and his side almost snuck a goal back when Gilks misjudged a Brunt free-kick, palming a delivery which was going out of play back into the six-yard box, but the chance was snuffed out.
But the away side's task became almost insurmountable when Jara became their second player to see red just before the half hour.
This time there was no doubting that Oliver made the correct decision as the Chilean defender needlessly scythed down Varney with a terrible two-footed challenge near the corner flag.
West Brom's night soured further when Marc-Antonie Fortune seemed to pick up a leg injury and was replaced by Graham Dorrans, who almost grabbed a goal back only to slice his effort wide.
Blackpool survived a scare shortly after the break when Craig Cathcart under-hit a pass and Dorrans won the ball to send Jerome Thomas on a quick break.
Cathcart immediately redeemed himself, however, with a diving block to keep out Thomas' goal-bound shot.
Blackpool were clearly intent on stretching West Brom's limited numbers with attacks down the flanks and that policy should have provided a second goal only for Varney to head a teasing cross straight into the arms of Carson from six yards.
With only a goal in the game West Brom had enough reason to retain some belief and after controlling possession for a 10-minute period started to push numbers forward.
It proved their undoing, however, as Blackpool found a second goal to give them a comfortable advantage in the 61st minute.
The industrious David Vaughan recovered the ball high up the pitch and quickly played in Grandin, who drove into the area and, with the exposed Carson committed to his near post, slid a pass across the face of goal for Varney to tap in.
That should have made the rest of the night comfortable for Blackpool but some poor defending allowed West Brom a way back into the game five minutes from the end.
Mulumbu was given too much time to trick his way into the area and curl a right-footed shot in at the far post to set up a nervy end.
The away fans suddenly sensed their side could snatch a remarkable draw and Scharner almost found it when he headed a Brunt free-kick narrowly wide before Reid blasted over following a goalmouth scramble.