Rafael Benitez’s men struggled to make an impact in the opening 45 minutes as both teams went in level at the break.
Burnley then stunned Everton by taking the lead in the 53rd minute through a Ben Mee header, but Michael Keane pulled the Toffees level just seven minutes later.
Townsend then got on the scoresheet five minutes later with a superb curling effort, while Burnley were left reeling just a minute after when Abdoulaye Doucoure played in Demarai Gray, who made it 3-1.
3-1 was how it finished and Everton have now picked up ten points from their opening four games to sit joint top of the table, behind Manchester United, Chelsea and Liverpool only on goal difference.
Townsend stressed that Everton have started well before only to fall away, something he feels they are better equipped to stop happening this term.
“We did not get close to Burnley in the first half, we were not giving Richarlison support and we rectified that”, he told BBC Sport.
“Dominic Calvert-Lewin has been the talisman and is a big loss but we have players in the dressing room who can step up.
“Michael Keane is one of the best finishers I have ever seen.
“Everton also had a great start last season too but fell away.
“We have suffered adversity in each game but have found a way to come out of it.
“That stands us in good stead for the rest of the season.”
Next up for Everton is a trip to Aston Villa, before then they head to the capital to play QPR in the EFL Cup.