Everton have been explosive at home this year, so only the most optimistic Burnley fans could have hoped for a first away win of the season. But Sean Dyche's team put in another improved performance, particularly in an excellent first half.
The Clarets were perhaps unlucky not to take the lead during that opening 45 minutes, but with top scorer Andre Gray relegated to the bench, they couldn't make the most of several chances that fell their way.
The hosts had needed a slice of luck to take the lead for the second time, after a Sam Vokes penalty cancelled out Phil Jagielka's opener, and a third soon after resigned Burnley to another defeat on the road.
But with a strong cushion and favourable results elsewhere, the Clarets are all but safe regardless.
The wait for that elusive win on the road continues, but this was another competitive performance. Earlier in the season, Dyche's team were overrun from start to finish, but since the turn of the year, they have at least looked like a solid Premier League side on the road.
It was always going to be an incredibly difficult game, but -- particularly in the first half -- Burnley took the game to Everton. For large periods, the visitors matched the home side, and with a bit of luck and composure could have been the first team in eight to take points away from Goodison Park.
Possibly their best away performance of the season, although that is an accolade with little competition.
The Clarets still look weak going forward. Without Gray, only Robbie Brady offered any real creativity. So when chances do come, it's important not to squander them. Too often the Clarets' offensive players waited too long to pull the trigger, or missed a crucial ball in the final third.
A more clinical side would have taken the lead in the opening period -- a situation neither side is used to being in could have dramatically changed the dynamic of the game. A striker should be at the top of Dyche's shopping list this summer.
Manager rating out of 10
7 -- Made the bold decision to bench Gray, whose impact has reduced in recent weeks. A front two of Sam Vokes and Ashley Barnes lacks dynamism, but made the team's structure more solid. It felt like that was the aim, with the emphasis on making life difficult for Everton. It largely worked, but you must also wonder whether Gray could have taken advantage of missed opportunities.
Player ratings (1-10; 10 = best. Players introduced after 70 minutes get no rating)
GK Tom Heaton, 7 -- Can feel hard done by for the first two goals and could do nothing to prevent the third.
DF Matt Lowton, 8 -- Continued his impressive form, solid throughout.
DF Michael Keane, 7 -- Impressive with the ball at his feet and could have scored in the first half, but he was beaten by the powerful Romelu Lukaku for Everton's third.
DF Ben Mee, 7 -- There was little he could do to prevent an unlucky own-goal.
DF Stephen Ward, 8 -- Like Lowton, he has really grown this season, and that continued today. Coped with Everton's strength and pace well.
MF George Boyd, 6 -- Made the game difficult for Everton but offered little going forward.
MF Joey Barton, 7 -- Misplaced a few passes, but, as ever always, recovered well. Controlled Burnley's game; the king of the second ball.
MF Jeff Hendrick, 7 -- Contained Everton well throughout without creating much in the Everton half. His form has picked back up in the past few games, after a short dip.
MF Robbie Brady, 7 -- Probably his best performance since returning to the Premier League in January.
FW Ashley Barnes, 6 -- A nuisance as ever. Caused headaches and bruises for Everton's defenders but never threatened Joel Robles in goal.
FW Sam Vokes, 7 -- Contributed to the impressive pressure going forward but probably should have scored from the run of play to go along with his penalty.
FW Andre Gray, N/R -- The game was over once he got onto the pitch. Little impact.
FW Daniel Agyei, N/R -- Ten minutes will boost his development, but he had no impact on the game.
FW Ashley Westwood, N/R -- Played out the last five minutes.