Celtic's Stilian Petrov moves in to block a shot by Charlie Millar of Dundee United at Tannadice Park yesterday.
Gary Breen's last-ditch header gave Coventry a dramatic victory that drags Everton into the dogfight at the bottom.
Coventry survived early Everton dominance and the aerial threat of Duncan Ferguson to come storming back in the second half to take the lead through Mustapha Hadji.
Everton hardly deserved anything for a wretched performance, but thought they had salvaged a point when Scot Gemmill drilled home a late equaliser. But two minutes later Breen struck with a powerful header, his first goal for almost three years, to send Coventry's animated manager Gordon Strachan crazy on the line.
Ferguson, still nothing like fit, was thrust into Everton's attack to underline the growing relegation concern on Merseyside. It was his first start of the season after persistent thigh problems had reduced him to just three appearances as substitute since his return from Newcastle in the summer.
Everton's start was predictable. Everything launched at Ferguson and on three minutes he reached a Gary Naysmith cross to force Chris Kirkland into what was the first of a string of saves.
But Coventry weathered the storm and started to create chances of their own. Coventry's more positive approach continued after the break as Everton became more aimless. A minute into the second period, Thompson wasted another glorious chance after a near pitch-length run from Craig Bellamy, which ended with the ball being squared across the box for the free-running Thompson to lash wide.
On 70 minutes it was the ever-improving Coventry who took the lead when Thompson's long free-kick into the box found Hadji charging into the box unmarked to head past Myhre.
Everton were resorting more and more to the long ball barrage in desperation, and Kirkland saved from a low, angled drive from Gemmill.
Everton thought they had salvaged something from a wretched performance when they equalised on 84 minutes when Steve Watson headed the ball forward for Ferguson to touch wide for Gemmill to drill past Kirkland on the run.
But Coventry just wouldn't give up, and were back ahead two minutes after Everton's goal when Breen headed home from another Thompson free-kick.
Everton: Myhre, Steve Watson, Weir, Ball, Naysmith, Gravesen, Gemmill, Pembridge (Nyarko 75), Tal (Unsworth 67), Ferguson, Cadamarteri (Moore 67). Subs Not Used: Simonsen, Cleland. Booked: Cadamarteri, Ferguson. Goals: Gemmill 85.
Coventry: Kirkland, Breen, Williams, Konjic (Edworthy 22), Quinn, Thompson, Telfer, Carsley, Bellamy (Chippo 84), Hadji, Zuniga (Aloisi 77). Subs Not Used: Eustace, Hydlgaard. Booked: Breen. Goals: Hadji 69, Breen 87.
Referee: N Barry (Scunthorpe).