Tony Pulis' men were on the front foot straight from the kick-off with Beattie and Ricardo Fuller combining to good effect up front.
And Fuller was heavily involved when former Hammer Matthew Etherington won the penalty which led to the opening goal in the 11th minute.
Etherington burst into the area to collect Fuller's back-heeled return pass and Julien Faubert felled the winger with a late challenge.
Beattie made no mistake as he rifled the spot-kick into the top right-hand corner of Robert Green's net for his first of the campaign.
The visitors retaliated with their trademark passing game and Carlton Cole's header from Alessandro Diamanti's cross was tipped over by Thomas Sorensen.
Stoke's normally solid defence was found wanting for West Ham's 34th-minute equaliser when Matthew Upson was allowed a free header from a corner.
Upson lost his marker Abdoulaye Faye from Mark Noble's left-wing delivery and, with Sorensen caught in no-man's land, the big centre-back made no mistake from seven yards.
Stoke were conceding possession too easily as the visitors, with their three central midfield players dominant, finished the half on top.
It was a similar story at the start of the second period as Diamanti's shot on the turn brought a diving save from Sorensen.
But Stoke responded to a rallying call from their supporters, with Beattie skinning James Tomkins to fire narrowly off target before a Ryan Shawcross header was blocked.
Both teams were now going hammer and tongs and it needed an outstanding challenge by Shawcross to deny Cole just a couple of minutes before Beattie's winner.
Fuller spun past Upson from Salif Diao's pass and made ground before firing a low shot from the right edge of the penalty area.
England keeper Green could only parry the effort and Beattie came in from behind Faubert to slide home the rebound from three yards.
West Ham gambled in search of an equaliser, but Stoke carried a real threat on the break as maverick Fuller twice went close to laying on a third.