Frank Lampard's side dominated from start to finish thanks to an influential display from Hakim Ziyech.
Luis Suarez partnered Diego Costa for the first time and scored as Atletico Madrid beat struggling Celta Vigo 2-0 in La Liga on Saturday.
Diego Costa scored his first goal since October but Atletico Madrid missed the chance to move into La Liga's top four by drawing 1-1 away at Athletic Bilbao.
Diego Costa was accused of failing to declare payments totalling over 5.15 million euros from his move to Chelsea in 2014.
Atletico Madrid's comfortable win puts them above Real Madrid in the La Liga table and level on points with Barcelona.
Diego Costa has agreed to pay 1.7 million euros to Spain's tax agency which was investigating him for non-payment of taxes on image rights.
Diego Costa had a hat-trick by halftime and added one more goal before he was sent off in the 63rd minute.
Diego Costa was sent off in the first half of Atletico's 2-0 defeat to Barcelona on Saturday for directing a crude insult towards referee Gil Manzano.
Costa sustained a thigh strain while playing for Atletico Madrid against Club Brugge in the Champions League on Wednesday.
Atletico Madrid scored two goals in extra-time to beat Real Madrid 4-2 in the UEFA Super Cup.
In Group B, Spain and Portugal are placed first and second respectively with four points each, while Iran is placed third with three points.
Diego Costa's physical presence and penalty-box prowess worked a treat for the Spanish as they ended a chaotic week with a thrilling 3-3 draw against Portugal.
Diego Costa killed Arsene Wenger's last hope of a glorious Arsenal farewell as his goal sent Atletico Madrid through to the Europa League final on Thursday
Diego Costa, 28, has been frozen out by Chelsea manager Antonio Conte and spent the transfer window angling for a return to former club Atletico that never materialised.
Exiled striker Diego Costa was not included in Chelsea's 25-man squad for the Champions League group phase on Monday.
The win over Middlesbrough left Chelsea seven points clear of Tottenham Hotspur at the summit and means they will be crowned Premier League champions for the second time in three seasons if they win at West Bromwich Albion on Friday.
Costa set up Eden Hazard's early opener, which was cancelled out by Oriol Romeu, before Gary Cahill restored the hosts' lead at an unseasonably cold Stamford Bridge.