Missing their talisman, in Dominic Calvert-Lewin, upfront, the Merseyside team had a difficult start to the game, being dominated by the Lancashire side till half-time whistle. Things kept going south for boss Rafael Benitez and his side after Burnley drew first blood in the 53rd minute through a Ben Mee header off a Johann Berg Gudmundsson cross.
But Everton weren't ready to give up yet as they upped the ante. The Toffees replied almost immediately as Michael Keane headed home a Townsend cross and levelled the scores. Soon after the English winger yet again made his impact felt as he stunned keeper Nick Pope with a thunderous long-range strike to give Everton the lead.
Everton's second-half attacking display was capped off by another clinical one-on-one finish from fellow new arrival Demarai Gray just a minute later.
After Mee ran through a crowd of blue shirts to head home from close range, Benitez immediately made a change to 4-3-3, withdrawing centre back Ben Godfrey for midfielder Andre Gomes, and the match changed in an instant.
Meanwhile, Doucoure featured heavily in the game as first he picked out Townsend from the halfway line and the winger cut inside onto his left foot to lash home a brilliant, looping, dipping shot.
He then sliced Burnley apart with a through-ball to send Gray racing through to make it 3-1 and the Frenchman was denied a deserved goal himself only by an offside flag as Everton ran riot.
It is four matches unbeaten now for Benitez and victory lifted Everton into fourth but level on 10 points with Manchester United, Chelsea and Liverpool.
However, going into the upcoming fixtures, Everton will be without their last season's highest scorer Calvert-Lewin, who is likely to be out for at least two to three weeks with a broken toe and thigh injury.