Middlesbrough edged closer to relegation to the Championship after losing 4-0 at Bournemouth following their latest limp display. In a match they desperately needed to win to boost their ever-diminishing chances of remaining in the Premier League next season, Middlesbrough were level for less than two minutes and collapsed thereafter.

Victory at the Vitality Stadium, followed by a further three points in the game in hand they are yet to play, may just have been enough to revive their season. Instead, one day after the death of the club favourite Ugo Ehiogu, they endured their latest miserable turn under the caretaker manager Steve Agnew, who has overseen four defeats and two draws since his appointment.

The result, which was worsened by the dismissal of Gastón Ramírez, also takes Bournemouth to the relative safety of 12th – seven points clear of the bottom three with four games to play.

The ease with which the hosts took the lead did much to demonstrate why it is Middlesbrough who look certainties for relegation. Their near-uncontested build-up on the left wing created space for Marc Pugh to cross to Joshua King, who from in front of goal and similarly under minimal pressure routinely finished low beyond Brad Guzan.

If Agnew had given Middlesbrough any belief before kick-off, it quickly vanished from then, after which Bournemouth’s fluid football posed a constant threat. In the 16th minute further poor defending led to a second goal. Uncertainty in possession on the edge of the area invited Harry Arter to dispossess Adam Clayton, and when the loose ball fell to Benik Afobe he struck beneath the onrushing Guzan and into the back of the net.

Bournemouth almost immediately again threatened to score, when Pugh’s classy backheel played in King, but the forward sent his shot over the crossbar. The frustrated Ramírez had already been booked for diving after an earlier challenge from Adam Smith when in the 20th minute he lunged in on Pugh and was given a second yellow by the referee Graham Scott, effectively putting a comeback beyond his team.

By the 29th minute, when Marten de Roon forced a fine diving save from Artur Boruc when shooting ambitiously from midfield off the bounce from Álvaro Negredo’s knockdown, the only question was what margin of defeat Middlesbrough faced.

Bournemouth played with patience and in the 65th minute Pugh extended their lead. A fine pass from the substitute Lewis Cook played him in, and from inside the area he curled across the face of goal and into the bottom-right corner. Their finest goal was also their last. After a 70th-minute free-kick was laid off to Charlie Daniels on the edge of the area, the Bournemouth left-back showed exceptional footwork to skip past Clayton before drilling low into the same corner as Pugh.

The Bournemouth manager, Eddie Howe, was full of praise for his players: “It was great to see our fluency with the ball,” he said. “That hasn’t been there in the last couple of games.”

Agnew, meanwhile, refused to concede relegation. “We have to be realistic,” he said. “It’s a huge challenge, but all we can do is dust ourselves down and get ready for Sunderland [on Wednesday]. Every game we need a win.”

Middlesbrough’s four other remaining fixtures this season are against Manchester City, Chelsea, Southampton and Liverpool, and they are 19th in the table, nine points from safety. There looks to be no way back.