Goals by Stephen Froggatt, Darren Huckerby and Noel Whelan elevated Coventry to 15th place and with the pounds 2.5m Norwegian striker Rune Lange reportedly on his way there is reason for optimism at Highfield Road, or at least to believe Gordon Strachan has arrested the recent decline.
After the loss of Dion Dublin to Aston Villa, it seemed things might rapidly turn sour for a side that began the season with European ambitions but two wins in two matches since their top scorer's departure suggests they can manage quite nicely without him.
Gerard Houllier may consider he has a job on his hands at Anfield but at least, unlike Everton's Walter Smith, he has not yet blown his cash. The former Rangers manager has spent more than pounds 21m since his arrival at Goodison Park in the summer, yet so far Everton look no less likely to struggle than last season, when only a point against Coventry on the final day clinched their survival.
Enjoying no shortage of possession, Smith felt they might have squeezed something from yesterday's match. But if Coventry had a weapon unavailable to Everton it was the electrifying pace possessed in large measure not only by the front-line partnership of Huckerby and Whelan but also by Stephen Froggatt on the left flank.
Football has not been altogether kind to the 25-year-old winger unveiled by Graham Taylor at Aston Villa seven years ago. After moving to Wolves in 1994 he appeared to be jinxed, suffering serious illness and then one injury problem after another. But his switch to Highfield Road six weeks ago offers a chance to relaunch his career.
Yesterday's goal, his first for his new club, will be a candidate for goal of the month. Chasing a clever pass out of defence by Roger Nilsson, Froggatt carried the ball a good 40 yards, leaving a pack of Everton pursuers well behind. Approaching the 18-yard line, he had the option to pass inside to Huckerby but chose instead to unleash a left-foot shot that ripped into the far corner of the Everton net.
In a half of open football, Everton should have replied with a goal of their own but their failure to do so perhaps reflected the same frailty of confidence as is afflicting Liverpool. Chances fell to Tony Grant, Duncan Ferguson, who sent a good heading chance wide from Don Hutchison's corner, and to the frustrating Ibrahima Bakayoko, at pounds 4.5m Smith's costliest signing, whose tendency to try to beat one defender too many is a habit he must curb.
A fine save from Magnus Hedman denied Grant what looked sure to be an equaliser after Alex Cleland's pull-back invited his team-mate to score from close range but Mhyre brought off a stop of equal merit to save from Gary McAllister close to half-time.
The killer blow for Everton came three minutes into the second period when pace again was the yellow-shirted visitors' enemy. Froggatt turned provider this time, his precise, driven pass finding Huckerby darting into the Everton penalty area. The Coventry striker's touch and finish were of the highest order.
Everton, with an injured Bakayoko giving way to Danny Cadamarteri, tried manfully to find a way back into the contest but, with McAllister more effective in midfield than his Scotland colleague John Collins, Coventry always looked the more likely source of more goals.
Myhre produced another excellent save to keep out a Froggatt volley and Whelan missed a golden chance 10 minutes from the end, hitting one effort straight into Myhre's body and scooping the rebound over the crossbar.
But Whelan enjoyed the last laugh, sliding the ball home in stoppage time after David Unsworth - one of three Everton players cautioned - had intercepted Huckerby's effort on the line after another lightning break from defence.
"It was not our worst performance but the second goal allowed Coventry to sit back and attack on the break," Smith said.
Goals: Froggatt (16) 1-0; Huckerby (48) 2-0; Whelan (90) 3-0.
Coventry City (4-4-2): Hedman; Nilsson, Williams, Shaw, Edworthy; Telfer, Clement, McAllister, Froggatt; Huckerby, Whelan. Substitutes not used: Breen, Boateng, Soltvedt, Shilton, Ogrizovic (gk).
Everton (3-5-2): Myhre; Short, Materazzi, Unsworth; Cleland (Milligan, 78), Grant, Hutchison, Collins, Ball; Bakayoko (Cadamarteri, 56), Ferguson. Substitutes not used: Watson, Dunne, Simonsen (gk).
Referee: G Poll (Tring).
Bookings: Coventry: Huckerby; Everton: Unsworth, Babayoko, Materazzi.
Man of the match: Froggatt.