In the absence of a specialist replacement, on-loan Arsenal midfielder Lansbury was summoned from the bench to reprise a role he briefly filled for England Under-21s last season after Robert Green was sent off for a professional foul on Blackpool substitute Roman Bednar in the 53rd minute.
At that stage United were 2-1 to the good following a dominant first-half display.
James Tomkins and Nicky Maynard scored two goals in four minutes, but Kevin Phillips brought the Seasiders back into the contest on the stroke of half-time.
But Ian Holloway's men rarely resembled a side on a seven-match unbeaten run and, with the exception of some routine handling that drew huge cheers from the away support, Lansbury was largely untroubled as Gary O'Neil and Ricardo Vaz Te completed a handsome victory.
West Ham are now one point ahead of Southampton at the summit with a game in hand, while Middlesbrough's victory at Millwall means Blackpool drop out of the top six.
Winger Matt Phillips returned form a hamstring problem to celebrate his Scotland call-up with a place in a Blackpool starting line-up that displayed five changes from the 2-0 FA Cup defeat to Everton on Saturday.
West Ham made two alterations to the side that drew with Southampton last week as George McCartney replaced the suspended Matt Taylor and Carlton Cole dropped to the bench for Maynard to make his full debut alongside fellow January recruit Vaz Te.
A clever Julien Faubert pass from the right flank gave Maynard a yard on the Blackpool backline, and the former Bristol City striker's low effort across goal was touched wide by goalkeeper Matt Gilks' outstretched boot.
Blackpool were struggling to establish any rhythm and when Ian Evatt fouled Maynard on the right in the 28th minute, the visiting supporters' chant of "We're gonna score in a minute" proved prophetic.
Mark Noble delivered the set-piece beautifully for Tomkins to plant a header past Gilks.
Moments later it was 2-0 as Jack Collison and Joey O'Brien combined down the right channel. Collison collected the scraps on the byline when O'Brien's cross was blocked, and cut the ball back to make Maynard's first West Ham goal a formality.
Holloway took action soon afterwards, introducing Kevin Phillips in place of Chris Basham, and the veteran striker gave Blackpool a lifeline they scarcely deserved in first-half stoppage time when he nodded home Alex Baptiste's speculative cross.
Seemingly buoyed by this success, Holloway sent on two further attacking options from his bench, with Nouha Dicko and Bednar replacing Ludovic Sylvestre and the frustratingly wayward Lomana LuaLua.
The contest was thrown wide open when Kevin Phillips' through-ball pierced the Hammers defence and Green charged rashly from his line to bring down Bednar.
Referee Oliver Langford was well placed and ignored the efforts of West Ham defenders chasing back, to brandish a red card.
Hammers boss Sam Allardyce turned to Lansbury and sacrificed Faubert.
Lansbury was impressively protected by the West Ham defence and with 16 minutes remaining substitute O'Neil lashed a crisp 20-yard drive into the bottom corner after Winston Reid's effort from Vaz Te's corner was blocked by Stephen Crainey.
Kevin Phillips then rattled the inside of the post with a lofted volley as Lansbury's positioning finally failed him, before Vaz Te raced clear of a largely absent Seasiders defence to open his Hammers account in the final minute.