The Blues had struggled to break down the visitors who could have taken the lead on a couple of occasions during the first period and they were unlucky not to lead at half-time.
But Negredo’s header on 65 minutes finally broke the deadlock and Toure’s superb free-kick on full-time sealed victory for Manuel Pellegrini’s side ahead of the international break.
After a week of defensive scrutiny by the media, a home win and a clean sheet was just what the doctor ordered, though this was by no means a comfortable 90 minutes for City who never really found their rhythm in the early afternoon Manchester sunshine.
Pellegrini kept faith in the majority of the side that went down 3-2 to Cardiff last weekend.
Losing to a newly-promoted side so early on in the campaign meant there was an urgency to get back to winning ways immediately if the feel-good factor generated by the stylish win over Newcastle was to return.
Back-to-back defeats to Premier League new boys was unthinkable.
Matija Nastasic returned at the expense of Javi Garcia, while Aleksandar Kolarov was recalled in place of Gael Clichy but it was Hull who started the brighter of the two teams, looking more relaxed and composed on the ball.
In contrast, the Blues were edgy and the play fragmented, but it could have been worse as Danny Graham played Sone Aluko clear with eight minutes gone but as Joe Hart raced out the Nigerian dragged his shot inches wide.
City responded immediately with Kolarov’s header from a Jesus Navas corner forcing Allan McGregor into a smart save.
Graham had the ball in the net two minutes later but had strayed offside, then Joleon Lescott went close with a header before Tigers’ skipper Robert Koren sent a half-volley inches wide, all in the opening 15 minutes.
The remainder of the half was frustrating as the Blues struggled to find their way past a well-organised defence.
Edin Dzeko made way for Negredo at the break and the Spaniard was guilty of a glaring miss just four minutes after the re-start as David Silva’s clever chip presented him with the simplest of headers but he got his angles completely wrong and headed well wide from six yards.
No matter. When Silva fed Pablo Zabaleta the Argentine produced a fine cross for Negredo to head home from close range with 65 minutes on the clock to at last break the deadlock.
Two headed goals inside a week suggests the former Sevilla man may not be starting from the bench for much longer – he looks made for the Premier League and adds a different dimension to the Blues’ attack.
It seemed the powerful Spaniard’s effort would prove to be the difference between the teams on the day, but Yaya Toure’s stunning free-kick on 90 minutes – a carbon copy of the goal he scored against Newcastle – sealed the points for Pellegrini’s men.
Nasri was fouled on the edge of the box and the Ivorian whipped a curling shot in off the underside of the bar to the delight of the sell-out home crowd.
The players can now head off to the international break with an element of relief, no doubt.
