Any sense they would miss their top scorer - officially injured but reported by British media to have had a row with manager Antonio Conte - lasted the six minutes it took Alonso to score with a right-foot shot after Eden Hazard's lay-off.
Pedro almost doubled the lead with a neat free-kick near the end of the half before Alonso struck again six minutes after the interval with a shot that deflected in off Leicester's Wes Morgan.
By that stage, Chelsea enjoyed almost complete control and Pedro wrapped up the win with a header from a move he began with an exquisite flick as the Blues restated their title credentials to restore their lead over second-placed Tottenham Hotspur, who beat them 2-0 in their last league game.
"That was a very professional, solid, good performance on the back of the Spurs game," said Chelsea's Gary Cahill.
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"I'm proud of the lads. It's all about not looking back."
Asked how difficult it was to cope without leading scorer Diego Costa, who missed the game through injury, Cahill said: "When someone is missing we produce, someone else comes in."
LEICESTER CITY 0 CHELSEA 3
(Reporting by Neil Robinson; Editing by Ken Ferris)
