Nagelsmann, whose sacking in March 2023 led to Tuchel's arrival, was tipped to return to Bayern, but has now extended his contract with Germany until 2026
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.