Light Blues striker Nikica Jelavic headed the Scottish champions into the lead after six minutes after being set up by Steven Naismith.
However, Chelsea soon asserted themselves and Sturridge, who had spent the second half of last season on loan to Bolton, struck twice to give the classy Londoners an interval lead which they never looked like surrendering.
Stamford Bridge substitute Florent Malouda, who had replaced Sturridge on the hour mark, headed in the third in the 72nd minute to emphasise the gap in class between the two sides.
The scoreline could have been worse for the home side had substitute goalkeeper Neil Alexander, on for Allan McGregor at the interval, not saved Frank Lampard’s penalty two minutes later.
The Premier League club will be pleased enough with this game as a warm-up for their Premier League campaign, which begins next week against Stoke.
Rangers, however, return to SPL duty against Inverness next week with plenty to think about.
Ally McCoist has had a difficult start to his career as Rangers boss and the lack of strength in his squad was highlighted when the team sheets came out.
Back in the Ibrox rearguard was Kyle Bartley, who returned for another loan spell from Arsenal earlier in the week. Jordan McMillan and Kyle Hutton were handed starts with the Light Blues’ bench packed with more youngsters.
Chelsea, on the other hand, had familiar star names such as Fernando Torres, John Terry, Salomon Kalou and Lampard in their starting line-up.
Their bench groaned with quality, including Malouda, Didier Drogba, Nicolas Anelka and Yossi Benayoun.
With former Rangers boss Walter Smith watching from the stand, the visitors took early control but it was the home side who drew first blood following a swift break from midfield by captain Steven Davis.
The Northern Ireland player played in the supporting Naismith on the right and when his cross arrived at the back post the unmarked Jelavic headed past the sprawling Petr Cech.
Chelsea stepped up the pace in response and in the 22nd minute they were level.
Torres worked his way in to the Ibrox box and the Rangers defence was all at sea when his cross found its way to the other side of the area where Sturridge blasted high past McGregor from 10 yards.
Moments later Torres tried a drive from distance which the Rangers keeper gathered at the second attempt but the second Chelsea goal was in the offing.
Just before the half-hour mark Sturridge robbed the hapless Kirk Broadfoot outside the Rangers box and sped in to the area before thrashing his close-range shot past McGregor at the near post.
In the 33rd minute the Scotland keeper made a fine save from Kalou’s shot, after the Chelsea attacker had been all too easily set up by Torres at the edge of the box.
There was a blow for the visitors two minutes before the break when midfielder John Obi Mikel limped off injured to be replaced by Josh McEachran.
Rangers made four changes at the break with McGregor, Jelavic, Bartley and Maurice Edu staying inside and Alexander, Ross Perry, John Fleck and David Healy coming on.
For Chelsea, Drogba replaced Torres and Jose Bosingwa came on Paulo Ferriage and there were, as expected, many more changes as the second half progressed which disrupted any discernible pattern of play.
In the 57th minute Rangers midfielder Juan Manuel Ortiz slashed a shot from 12 yards wide of the target but the Londoners remained in control and Drogba came close with a drive in the 66th minute which just evaded the far post.
However, the next goal arrived soon enough when Drogba flicked the ball on to Malouda who headed past Alexander from close range.
Two minutes later Chelsea were awarded a penalty when Ortiz clumsily tripped Drogba in the box but Alexander guessed right and dived to his right to save Lampard’s spot-kick.
The Ibrox number two made further saves from Anelka – another Chelsea substitute – and Drogba, to show McCoist that the goalkeeping department is perhaps the strongest part of his squad as he looks forward to what is sure to be a testing season ahead.