The hosts took that 2-0 lead into half-time but, when a stuttering second half finally came to life, Shawcross profited from Danny Murphy's lax far-post covering at a corner to head home.
Fulham handed a debut from the start to new Russian import Pogrebnyak alongside Bryan Ruiz in an attacking line-up bereft of defensive midfielders, Danny Murphy the deepest in the middle. The Potters, meanwhile, brought in Matthew Upson at centre-back for the suspended Robert Huth with Kenwyne Jones partnering Peter Crouch up front.
Fulham attempted to play around new signing Pogrebnyak from the start. Thirteen minutes into a chance-light opening period, Dembele slipped a canny ball down the left of a crowded penalty area for Damien Duff, who crossed low in search of the Russian but Sorensen dived on the ball in goal before the forward could reach it.
Pogrebnyak had better luck two minutes later. John Arne Riise’s long-ranged shot was blocked but dropped at the striker’s feet on the edge of the area, and the former Stuttgart man took aim and thumped a left-footed shot into the roof of the net to open his Cottagers account.
The adrenaline from the goal, however, seemed to overcome the striker when he crashed into Wilson Palacios shortly afterward, completely missing the ball and clumsily bringing the Honduran down. The blond hitman was very fortunate not to receive a booking or worse for his reckless challenge.
Stoke started forging opportunities after the goal but neither Jones nor Palacios could conjure shots that came near the target.
However, it was Fulham who patiently passed the ball around the midfield, waiting for space, before Dempsey found himself with time to tee himself up and few defenders in his way. The American launched a stunning shot that swerved both ways in the air as it flew onto the bar via a very slight touch from Sorensen, only to hit the keeper as it came back and drop into the net.
The home side continued their dominance as Pogrebnyak powered into the penalty area down the left channel, aiming a pass into the middle for a waiting colleague, but Upson accelerated well to cover and head the ball away.
Dempsey was then tripped by Andy Wilkinson on the edge of the area, allowing Murphy to take a free-kick from an inviting angle, but, after using Dembele to tee himself up, the wily midfielder’s shot dropped wide.
Fulham kept coming, though, as a long ball into the area evaded Wilkinson, allowing Duff to have a snapshot at the far post, but Sorensen reacted quickly to deny the Irishman.
After the break, the hosts picked up where they left off in terms of possession and threatened when Duff fed Stephen Kelly on the overlap. The full-back’s cross hovered dangerously close to the net before Sorensen parried it well.
Pogrebnyak was then felled just before the hour as he fell awkwardly on his ankle. The Russian recovered well enough to return to the pitch a moment later but was swiftly substituted for Simon Davies anyway, with general match fitness also a concern on his debut.
With Dempsey moving into the centre-forward role as a result, Riise searched him out with a cross from the left into the box – the American was well-placed to deliver but seemed surprised that the ball had reached him and not Davies ahead of him, and the chance was spurned.
Substitute Jermaine Pennant showed signs of life for Stoke and whipped in a testing ball from the right wing in search of Upson and Palacios, but neither could capitalise on the header.
And the visitors got back into it with just over 10 minutes left when Shawcross ran in at the near post to flick a corner on with his head. It should have been stopped at the far post but the experienced Murphy wandered off his line and the Stoke defender profited.
In the end, though, the Cottagers should have extended their lead as Dempsey was let loose through the middle thanks to a poor attempted clearance by Upson. The American, however, was thwarted again by fine reactions from Sorensen at his feet.
Dempsey then had another late chance as he escaped Sorensen on the counter and had an open goal to aim at from the left of the pitch, but he rolled it against the post. The final whistle accompanied it, though, to consign the visitors to another defeat.