Here's our take on a dominant performance at the Bridge... https://t.co/zErF9MiduH— Chelsea FC (@ChelseaFC) May 8, 2017
Alonso added the second 11 minutes later, sliding in to divert the ball in through Guzan's legs after a cross from Cesar Azpilicueta.
Chelsea continued to control the contest after the interval and Nemanja Matic sealed the win with a powerful shot 25 minutes from time.
Antonio Conte's team, seven points clear with three matches left to play, can wrap up the title with a win over West Bromwich Albion in their next match on Friday night.
Middlesbrough, meanwhile, return to the Championship after one season in the top flight.