Sturridge's strike in the 47th minute effectively killed off the tie in what was Darren Ferguson's first home match as manager.
Ferguson will no doubt look back on a chance that changed the face of the game.
Darren Carter should have cancelled out the opening goal from Nicolas Anelka but somehow screwed his shot wide of the target.
Chelsea controlled the game and had it not been for goalkeeper Andy Lonergan the margin could have been greater.
The visitors almost took the lead in the 14th minute when Yury Zhirkov saw his effort booted away by Lonergan after the Russian international had played a neat one-two with Frank Lampard.
That came after an early scare when Hilario punched away a header from Chris Brown following a cross from Chris Sedgewick.
Chelsea began to impose themselves and Anelka got into a good position only to drag his effort wide of the target.
Preston were struggling to get into the game but Callum Davidson found himself clear in the area. However his soft header ended in the goalkeeper's arms.
Then substitute Florent Malouda found the net for Chelsea in the 26th minute but instead of celebrating a goal they were awarded a free-kick on the edge of the area.
Michael Ballack saw his effort deflected to safety but this was an difficult spell for Preston.
The home side were grateful to Lonergan five minutes later when he stood tall to parry Alex's blistering 25-yard effort following a short free-kick from Lampard.
Chelsea's pressure paid off when Anelka made the breakthrough. The France striker got away from Youl Mawene on the edge of the box and even though Lonergan made some contact he could prevent his effort going into the net.
Preston, however, launched a spirited comeback and nearly drew level four minutes later.
Brown's towering header was taken by Hilario at the last moment and the ball fell to Carter but he found the wrong side of the post with the rebound.
Play switched down the other end and Paulo Ferreira almost extended Chelsea's lead with a blistering shot that went narrowly wide.
Chelsea doubled their advantage two minutes into the second half following a corner from Malouda.
John Terry powered in a header that came back out but only as far as Sturridge, who whacked the rebound home.
Sturridge then had an appeal for a penalty waved away after he went down in the area following a challenge from Davidson.
Ferguson decided to take off the unfortunate Carter in the 59th minute and bring on Jon Parkin to add a bit of muscle up front.
Chelsea were looking comfortable with a two-goal cushion and Anelka tried to release Sturridge but he had strayed offside.
Ballack tried his luck from distance but the ball hit Lampard's heel before Sturridge almost got a second goal, his effort going marginally off target.
Lonergan again came to Preston's rescue in the 67th minute, pushing over a header from Ballack inside the six-yard area.
Preston striker Parkin then tested Hilario from distance in the 77th minute as they tried to get back in the game.
Parkin was not afraid to shoot on sight and saw his effort minutes later sail wide of the target.
Sturridge went close again in the 83rd minute and substitute Joe Cole fired wide late on as Chelsea ran out two-goal winners.