Tony Pulis' side gave their all, but it never looked likely to be quite enough against top-quality opposition.
Chelsea had injuries with Ricardo Carvalho, Deco and Joe Cole all absent, but Stoke had to counter a big problem themselves with long-throw specialist Rory Delap ruled out with a hamstring strain.
Predictably, Chelsea gained a massive percentage of the possession and Thomas Sorensen was soon forced to tip over a 20-yard screamer from Michael Ballack.
And Sorensen made a tremendous save to deny Didier Drogba in the 14th minute after racing from his line to narrow the angle after Frank Lampard's slide-rule pass had sent him on his way.
Stoke, as usual, were contesting every inch of turf and Mamady Sidibe was proving a menace on the odd occasions Pulis' side were getting into the final third.
But Chelsea's pressure finally paid in the 36th minute in a move started and finished by Jose Bosingwa.
The Portugal international right-back eventually burst onto Lampard's telling pass to drive a shot across Sorensen and into the far corner of the net, despite Andy Griffin's attempt to clear off the line.
Chelsea twice went close to extending their advantage early in the second half as Lampard's shot drifted inches wide and a fierce drive from Florent Malouda smashed against the Stoke crossbar.
And Stoke came close to making them pay as they enjoyed their best period of pressure followed the introduction of substitute Ricardo Fuller in the 53rd minute.
Leon Cort rose highest to Liam Lawrence's right-wing corner on the hour but the big defender's firm header was cleared off the line by John Obi Mikel.
But Cort was culpable as Chelsea ensured there would be no anxious finale, with substitute Nicolas Anelka making the points safe 14 minutes from time.
Cort stumbled as he attempted to deal with the excellent Bosingwa's right-wing delivery and Anelka struck a first-time shot which brushed Sorensen's fingers on its way in.
Chelsea could afford the luxury of seeing Lampard squander a simple chance by his high standards in the closing stages as Stoke, who gave absolutely everything, finally ran out of steam.