Ancelotti's side had trailed to Babatounde Bello's shock 19th-minute opener for the Group F minnows but Sturridge levelled six minutes after the break.
Malouda then grabbed a vital winner for the Barclays Premier League champions when he slotted home at the far post four minutes from time to ensure Chelsea finish in top spot.
Zilina, battered by Marseille in their last Champions League outing, had arrived with an attacking mentality that gave Chelsea's youthful side something to worry about in the early stages.
Chelsea first threatened the visitors in the 17th minute when Gael Kakuta sent over a cross that almost dropped into the net at the far post.
But Chelsea hit trouble in the 19th minute when Bello sliced his way through the home defence and coolly slotted the ball home.
It was another shock to the Blues who have been left reeling in recent weeks by events both on and off the pitch.
The shock and abrupt departure of Ray Wilkins arrived in the middle of a domestic slump that has seen them lose three out of their last four Premier League games.
Ancelotti, who rejected rumours he was set to quit the Blues over the weekend, cut a lonely figure in contrast to the delirious Zilina bench.
Chelsea fought back when Kakuta put Sturridge in behind the defence but the former Manchester City striker saw his shot slash wide of the near post.
But Zilina almost added a second on the half-hour when Tomas Majtan got clear to test Ross Turnbull at the near post. The Chelsea keeper was lucky to claw the ball away from danger as Zilina continued to threaten.
Seconds later Sturridge forced Martin Dubravka into a fine save when he sent a 20-yard angled drive towards the top corner.
Malouda should have levelled the scores in the 35th minute but he sent a tame header into the arms of Dubravka from six yards.
Malouda then tried his luck from 25 yards but he failed to find the target.
Sturridge wasted another chance in the 39th minute when he somehow sent a six-yard shot over the bar, although Chelsea were at least beginning to exert some pressure.
Chelsea replaced Kakuta with Salomon Kalou at half-time and the Ivory Coast striker sent a shot just over the bar from 20 yards straight from the re-start.
Chelsea equalised in the 51st minute when Kalou's cross eluded everyone in the six-yard box apart from Sturridge at the far post, the striker slipping the ball through the legs of the Zilina keeper to make it 1-1.
Chelsea were now in the ascendancy and Ramires sent a 25-yard drive just past the post as the Blues increased the tempo.
Didier Drogba almost put Chelsea in front on the hour but his free-kick was tipped onto the crossbar by Dubravka and Branislav Ivanovic headed over from close range when the ball was played back into the area.
Chelsea were now dominating and pushed on in search of the winner.
In the 69th minute Sturridge curled a low shot around the post after Chelsea has superbly carved open the Zilina defence.
Patrick Van Aanholt was denied by the woodwork in the 71st minute when his thunderous 20-yard drive cannoned back off the left-hand upright.
Midfielder Josh McEachran, who had been sublime all night with a range of delightful passes, put Drogba clear in the 75th minute but the striker fired high over the bar.
But Chelsea ensured they maintained their 100% record in Europe when Malouda slotted home at the far post after Drogba had headed substitute Nicolas Anelka's cross into his path.
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