Just as in the defeats at
the Tigers never looked overawed and even as they slipped to a third loss of the season, this was a display that will add to their belief that they can stay in the Premier League.
Barry tackle on Aluko angers Bruce
Everton striker Romelu Lukaku had already had a low effort held by Allan McGregor before the hosts went ahead after seven minutes.
Hull failed to clear a Baines corner and Leon Osman squared to Mirallas, whose low effort flew past Gareth Barry, standing in an offside position, and the motionless McGregor into the bottom corner.
Tigers manager Bruce, who was also angered by a couple of challenges by Barry, felt the goal should not have stood whether the Everton midfielder touched it or not.
Everton never looked comfortable at set-pieces and the unmarked Abdoulaye Faye missed two good openings from Tom Huddlestone and Robbie Brady corners.
Hull moved level when Aluko beat Baines and clipped over a low cross for Ivorian Sagbo, a
summer signing from Evian,
to thump in at the near post for his first Premier League goal.
Just before the interval, Aluko had a drive deflected over by Sylvain Distin and then had a header blocked on the line by Baines after Faye once again got his head to a Huddlestone corner.
Martinez's side controlled possession from the start of the second period but Hull almost took the lead when Jake Livermore's drive glanced wide off Sagbo.
But Pienaar's introduction swung the game back in Everton's favour, with the South African turning in a first-time shot from Mirallas's cross to finish a slick passing move that started with goalkeeper Tim Howard.
Faye and Davies had further chances from corners before Arouna Kone missed a fine chance to add a third for Everton when he hit the post from six yards from Seamus Coleman's cross.
Everton manager Roberto Martinez:
"I've watched it six or seven times and it's impossible to tell [whether Barry got a touch]. Even if he touched it minimally the referee couldn't see it. If the referee's not sure he has to let it go.
"When I saw [Barry's tackle on Aluko] live I felt he won the ball. The pitch was open to those sorts of challenges. The referee handled it in a common sense manner and was consistent.
"It wasn't our normal stylish way but we got the three points."
Hull manager Steve Bruce:
"The big decisions went against us. Gareth Barry ran away celebrating the goal and that indicates he touched it. Even if he hadn't he was interfering.
"Gareth Barry is a fantastic pro but his tackle on Aluko was a red card. Those tackles that are over the top of the ball can badly injure people. The big decisions went against us and you expect the officials to get them right. The Aluko challenge was a disgrace.
"The positives have been there all season. We are a good group that are desperate to do well and we'll make a fist of it I'm sure of that."
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