Roberto Martínez is a manager who has sent on a replacement and watched him score the winner in an FA Cup final but he can rarely have seen a substitute succeed so quickly. Twenty-seven seconds separated Steven Pienaar's introduction and the midfielder's decisive goal. "He finds the back of the net with his first touch," Martínez said, smiling. "It is quite an impact."

On an occasion branded Retro Day, perhaps it was fitting that the winner came from a player who had revisited his past by returning for a second spell at Everton. Nevertheless, this is a new era and Martínez has made an auspicious start. With 15 points from eight games, they continue to savour the sight of a league table that has Manchester United, and their former manager David Moyes, sitting beneath them.

If Gareth Barry, whose four league appearances have ended in victory, has been pivotal, the catalyst was also the cause of controversy. "Nobody is more of an admirer of Gareth Barry than I am," said the Hull manager Steve Bruce, prefacing the airing of his grievances about the midfielder. They were threefold: that Barry scored Everton's opening goal and rendered it illegitimate; that he escaped without a card for the foul that meant Danny Graham was carried off with a seemingly serious knee injury; and that referee, Neil Swarbrick, only cautioned him for a worse challenge on Sone Aluko.

Everton's opener was credited to Kevin Mirallas. Teed up by Leon Osman, the Belgian drilled in a shot from 20 yards, his shot clipping the inside of the post as it beat a static Allan McGregor. Barry, who found himself in its path, was rather more active, trying a backheel flick. "He is a yard offside and he touches it: 100%," Bruce said.

Then Barry became the unlikely destroyer. Both members of Hull's strike partnership felt the force of his tackling. "The one on Danny Graham is bad enough," Bruce said. "That is worthy of a yellow card. But the challenge on Aluko is absolutely horrific. It is over the top of the ball."

Martínez, citing the slippery surface, argued that the referee was right to be lenient. He said: "I feel it was right to give a yellow card. I think the referee understood the conditions."

Bruce disagreed, arguing that both victim and assailant were lucky in different ways. The surprise that Aluko was able to continue was amplified when, with a swift change of pace, he fashioned Hull's equaliser. He darted to the byline, crossed and Yannick Sagbo finished adeptly. It served as a reminder that every injury is also an opportunity; whereas Graham, infamously, has been unable to score in the league since New Year's Day, his replacement opened his Hull account.

It was a sign of Hull's resourcefulness. They targeted Everton at set pieces, where their sizeable centre-backs Curtis Davies and Abdoulaye Faye won a series of headers and both the Senegalese and Aluko came close to scoring.

Yet Everton, too, could take the direct route. Their winner was a strange blend: part Moyes's tactic of aiming a long ball at a Belgian – Romelu Lukaku heading on Tim Howard's punt – and part the slick, quick passing football that Martínez prefers. Ross Barkley and Mirallas combined with the winger directing a cross for Pienaar, displaying perfect timing, to pick out the corner of the net.

"It was very important for us to have that little bit of magic to get that second goal," Martínez said. It was not merely Pienaar's first touch of the game, but his first since August. A hamstring injury had sidelined the South African and Martínez had been inclined to omit him altogether. Pienaar's sharpness in training proved persuasive, however, and Martínez, whose first change brought a goal, brought on Arouna Koné and the newcomer hit the post. There was no action replay; no second scoring substitute.