Managerless Hull's miserable Championship run continued with a 3-1 loss at Middlesbrough, their fifth straight league defeat.
Andy Dawson was in interim charge of the Tigers after Tim Walter's midweek dismissal but couldn't stop the rot, with City now winless in their last 10 league games.
Finn Azaz continued his superb run of form with a fifth goal in three games to set Boro on their way, before Tommy Conway doubled the home side's lead just before half-time.
Hull substitute Mason Burstow gave the Tigers hope when he halved the deficit 19 minutes from time, but Conway secured the points with his second and Boro's third goal eight minutes later.
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Carrick's side have now won four of their last five games and are the Championship's top scorers.
Boro had the first clear cut chance of the game when Azaz crossed for Delano Burgzorg but the forward completely miskicked his effort when he only had Hull keeper Ivor Pandur to beat.
Boro were perhaps fortunate at the midway stage of the first half when defender Neto Borges - the last man - appeared to have a pull at the shirt of Joao Pedro, who was prevented from running one-on-one with goalkeeper Sol Brynn. Referee Stephen Martin waved away the claims.
And Hull's frustration deepened when Azaz curled in the opener on 24 minutes. There was still plenty of work to do when the former Aston Villa man collected the loose ball on the edge of the box after Hayden Hackney intercepted an attempted Hull clearance. But he calmly cut back on his left foot to create a shooting opportunity for himself and beat Pandur.
It was the home side's turn to complain to referee Martin shortly after the half hour mark when Ben Doak claimed his cross hit the arm of Xavier Simons after a swift Boro counter, but the protests were dismissed. Doak's anger was short-lived, for it was the Liverpool loanee who created Boro's second goal four minutes before half-time.
After Anfernee Dijksteel won back possession on the right side of the box, Doak lifted a delightful lobbed cross on to the head of his Scotland teammate Conway.
Hull could not cope with Doak and captain Lewis Coyle almost sliced the ball into his own net as he attempted to clear a cross from the winger early in the second half. Doak then created a shooting opportunity for himself but saw his effort deflected wide.
Hull gave themselves hope when the unmarked Burstow turned in Abu Kamara's cross from the left. But Conway wrapped up the points with a tidy finish after Doak's pass.
The managers
Middlesbrough's Michael Carrick:
"Today was a tough game, and we expected it to be that way. The type of team they are, the quality they've got and the way they play.
"The change in manager can go in different ways and adds an element of uncertainty as well, so I expected we'd have to really work for it. Those type of games can become quite hard because you're chasing it and they have the quality to keep the ball off you.
"It can be a tough afternoon. But the boys stuck at it because it wasn't easy to have an exact plan for it and we had to focus more on just what we could do in terms of our shape and distances and the feeling between each other.
"The boys stuck at it and did the good things to get the result. It was a tricky game but one we came through really well. We did a lot of things well - pressed well, scored good goals and probably could and should have scored more. All in all, it was good to bounce back from what will hopefully now prove just a blip in midweek."
Hull's interim boss Andy Dawson.
"It's difficult because emotion always run deep when you're on the run that we're on.
"We've lost another game. I feel the pain and all the staff do, we're feeling it, of course we are.
"When I take myself away from the disappointment and ask did they do what we asked of them? Yes, they did.
"I have to give credit to Middlesbrough, they're a very good team who can hurt you and score goals. But there is lots of work to do, absolutely. We have to go again."