Harry Kane marked his return from injury with a goal and Vincent Janssen netted his first in the top flight from open play as Mauricio Pochettino's men continued their impressive form.
Mousa Dembele and Heung-min Son were also on target, while top-four hopefuls Manchester City gave their Champions League chances a lift with a 3-0 win at Southampton.
Down at the bottom, Hull and Swansea suffered defeats as others pulled away in the race for Premier League survival.
FULL MOTD RUNNING ORDER (10.20pm - 11.45pm)
Everton 3 Burnley 1
The relegation battle will in all likelihood now come down to a straight shootout between the two sides after Crystal Palace and West Ham both took a point.
The Eagles were 2-0 down at home to Leicester, but launched a second-half comeback to rescue a point with goals from Yohan Cabaye and Christian Benteke.
The Hammers led 2-1 in the dying minutes at the Stadium of Light as they gifted David Moyes's strugglers a lifeline.
Fabio Borini pounced on Darren Randolph's error before Sam Byram was dismissed.
Chelsea travel to Manchester United on Sunday after West Brom host Liverpool, while Arsenal visit the Riverside on Monday evening.