The German tactician was brought in to replace Frank Lampard early last week and began his reign with a goalless draw against Wolverhampton Wanderers at the Bridge.
Against Sean Dyche’s men who arrived in West London with impressive back-to-back victories over champions Liverpool and Aston Villa, Chelsea looked in total control and the game ended with no shots on goal from the Clarets.
Chelsea’s first half dominance paid off five minutes before the break, when Azpilicueta expertly finished off a pass from Callum Hudson-Odoi.
The hosts’ second goal did not arrive until the 84th minute and it came courtesy of forgotten man Alonso, starting his first Premier League since September last year, who expertly controlled Christian Pulisic’s through pass in the Burnley box before blasting an unstoppable strike past Nike Pope.
Chelsea’s victory has taken them to seventh place on the league log with 33 points while Burnley are in 16th place, eight points above the relegation places.
The Blues are next in action against Tottenham Hotspur next Thursday while Burnley will host leaders Manchester City a day earlier.