Preston North End 0 Chelsea 2
The Lilywhites made a bright start in front of their own fans, with a header back from Chris Brown almost finding Richard Chaplow, before Blues keeper Hilario got a crucial touch.
However, the Premier League side then began to settle and a classy one-two between Yuri Zhirkov and Frank Lampard saw the latter fire goalwards, with Andy Lonergan making a fine block at his near post.
Just past the half-hour mark Lonergan was forced to parry a stinging 25-yard free-kick from Anelka, as the visitors continued to look the more threatening of the two sides.
Eight minutes before the interval Chelsea made the breakthrough, as Anelka cut in from the right and his low drive from 15 yards was deflected past the unsighted Lonergan.
Preston should have been level soon after, but Darren Carter lifted the ball over the top from a couple of yards after Hilario could only tip away Brown's far-post header.
The home side paid for that miss soon after the restart when John Terry met a right-wing corner from Florent Malouda and although Lonergan blocked the initial header, Sturridge powered home the rebound from close range.
The second goal seemed to quell the home side's resistance and Michael Ballack almost made it 3-0 with a fierce shot which was tipped over by the over-worked Lonergan.
Sturridge then drove a long-range shot narrowly wide with just under 20 minutes to play, before Lonergan got down smartly to field another effort from the impressive Anelka.
Joe Cole curled a late effort narrowly wide from the edge of the area as the Blues finished the game well on top.