An equaliser from 21-year-old Daniel Sturridge and assured displays from 17-year-old midfielder Josh McEachran, 19-year-old defender Jeffrey Bruma and 20-year-old defender Patrick van Aanholt in the second half helped Chelsea to victory after going behind in the 19th minute.
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Zilina went ahead through Babatounde Bello and held that lead until six minutes into the second half when Sturridge equalised with a close range effort in Chelsea's 100th match in Europe's elite club competition.
The London side then dominated the second half before finally getting the goal they deserved through Malouda's tap-in four minutes from time.
"We did not play well in the first half but we were very good in the second half and I was very pleased with the young players generally," Ancelotti told reporters.
"It was important to win and move on. We have now had 60 shots at goal in our last two games but only scored twice. We have been unlucky not to score more but the young players have had some good experience tonight and showed the quality they can bring to the team."
"He was good defensively today but can play the ball long or short without a problem," he said. "He has to grow, he has to improve - but he is ready to play."
Chelsea hardly looked ready for anything much in the opening half but it was still a surprise when they fell behind when Bello, a 21-year-old Nigerian-born Benin international exchanged passes advancing up the field with Robert Jez before firing wide of goalkeeper Peter Cech's stand-in Ross Turnbull.
That was Zilina's first goal in the competition since their 4-1 home loss to Chelsea in September, and they continued to worry the English champions.
