Huddersfield Town were sucked right back into the Premier League relegation battle after they succumbed to a 2-0 defeat at home to Everton.
Cenk Tosun's first-half goal put Everton on course for a second successive victory and Idrissa Gueye scored in the second half to wrap up a win that extends their unbeaten streak to four games.
Fortunately for Sam Allardyce's men, Huddersfield struggled to cope with the pressure of needing three points to all but secure their place in the division next season, defending nervously and failing to capitalise on the few clear-cut chances they created.
Tosun's goal arrived courtesy of an incisive run from the tireless Theo Walcott, but the Turkey forward still had plenty of work to do to score and his finish showed class under pressure, while Gueye had an easier task and scored with aplomb.
Town's last three games of the season will see them travel to Manchester City and Chelsea before finishing the campaign at home to Arsenal, and Wagner will be furious that they squandered the opportunity to pick up points against an Everton side with far less to play for.
The defeat leaves Huddersfield just three points above the drop zone after Southampton's crucial win against Bournemouth.
It took until the 16th minute for either side to register a meaningful effort, Town striker Steve Mounie striking tamely at Jordan Pickford from just outside the area.
Terence Kongolo blazed over the crossbar from the edge of the box from a corner shortly after, but the Terriers largely lacked urgency.
Wayne Rooney, without a goal in 2018, curled a shot harmlessly wide as Everton finally bared their teeth, while a counter-attack at the other end saw a surging Alex Pritchard cut back for Rajiv van La Parra from the right, but the Dutchman powered a first-time effort over the crossbar.
And, just as the hosts appeared to garner some momentum, Everton went in front.
Walcott burst down the centre and sprayed a pass to the right of the area where Tosun drilled a low shot into the far corner, narrowly evading Jonas Lossl's hand on the way in.
Everton started the second half with the wind in their sails and Nikola Vlasic thumped a low shot towards goal from the edge of the box that Lossl did well to hold.
Seamus Coleman missed a golden chance to double Everton's lead when he got in behind the Huddersfield defence at a free-kick and had two passing options as well as the whole goal to aim at but his first touch was poor, knocking the ball straight into the grateful arms of Lossl.
Pritchard was presented with a chance to equalise when Van La Parra's cross from the right found him unmarked in the box but his feet appeared to get caught in the turf and his attempt at a shot had the home fans groaning.
Town were probing for an equaliser when the game drifted out of their reach as Everton substitute Oumar Niasse crossed from the right and Leighton Baines squared the ball to Gueye, who thundered the ball into the bottom-right corner of the net to make sure all three points went over the Pennines to Merseyside.
Key Opta stats:
- Everton have won two of their last three Premier League away games (W2 D1 L0), more than they had in their previous 23 on the road (W1 D9 L13).
- Indeed, they have picked up just one fewer point away from home in their last three games (7 - W2 D1 L0) than they had in their first 15 on the road this season (8 - W1 D5 L9).
- Huddersfield have failed to score in 19 different Premier League games this season, the joint-most by a promoted side in their debut season in the competition (level with Cardiff in 2013-14).
- This was Everton's first away win in the league by more than one goal since Boxing Day 2016.
- Cenk Tosun scored his fourth away Premier League goal of the season – no Everton player has scored more on the road in 2017-18 (level with Wayne Rooney).
- Leighton Baines has been involved in 82 Premier League goals for Everton (29 goals, 53 assists), behind only Romelu Lukaku (91) and Duncan Ferguson (83) for the Toffees in the competition.