The damage was done in the opening half with two goals from Nicolas Anelka and another from Michael Essien.
Daniel Sturridge added a fourth early in the second-half before Tomas Oravec scored a consolation for the home side.
Zilina began impressively with Momodou Ceesay firing high over the bar in the fourth minute.
The small ground was at its capacity of 11,000 and the home side were giving their fans something to shout about in the early stages.
Chelsea won their first corner in the ninth minute but Yossi Benayoun sent his shot into the arms of Martin Dubravka.
The English champions then wasted a free-kick on the left edge of the penalty area when Sturridge fired high over the bar from 20 yards.
But the Blues went in front in the 13th minute with a simple goal. Essien put Anelka clear on the left wing and when the cross arrived, Florent Malouda stepped over it for Essien to fire home from eight yards. It was the Ghanaian’s third goal in two games.
Zilina almost levelled in the 15th minute when a free-kick from Robert Jez was fumbled by Petr Cech but the Chelsea goalkeeper managed to stop the ball going into the net.
Zilina’s Bello Babatounde then headed straight at Cech in the 23rd minute after a fine cross from Ceesay.
But Chelsea went 2-0 up in the 24th minute when Malouda put Anelka clear and the former France international slipped the ball under Dubravka.
Sturridge almost made it 3-0 in the 27th minute but his 25-yard drive was tipped around the post.
But the Blues punished the home side from the corner which followed when John Terry’s header hit the bar and Anelka pounced to score his second from point-blank range.
Malouda should have made it 4-0 in the 37th minute but his shot was blocked by Mario Pecalka after Yury Zhirkov had pulled the ball back to him from the touchline.
Cech was forced to make a fine save four minutes from the break when he dived to push a shot from Admir Vladavic to safety.
Zilina then squandered a real chance when Babatounde headed wide from an unmarked position on the edge of the six-yard box.
However, Chelsea increased their lead in the 48th minute when Benayoun played a superb ball through for Sturridge who rounded the Zilina goalkeeper and slipped the ball home.
Zilina responded immediately and Cech was forced into a fine save to deny Vladavic.
The home side finally reduced Chelsea’s advantage in the 55th minute when Cech spilled a cross and the ball rebounded off Branislav Ivanovic before Oravec bundled home.
Zilina then went close to getting a second when Vladavic sent a rising drive just wide and substitute Tomas Majtan was inches away from hitting the target with an angled drive in the 65th minute.
Chelsea were living dangerously, but with a three-goal cushion they could afford to.
Ancelotti was distinctly unhappy on the touchline as the home side attacked in numbers.
The Slovakian home side had to be admired for their endeavour although Chelsea were hardly in top gear in the second half.
With 10 minutes left, Chelsea opted to hand a full debut to 17-year-old midfielder Josh McEachran. He replaced Benayoun who was applauded off for his fine performance.
Essien forced a fine save from Dubravka in the 82nd minute as the Ghanaian midfielder looked for another goal but it was the last real action of the game as Chelsea ran out easy winners.