Frank Lampard’s side are the first club in 127 years to secure successive English top-flight victories immediately after losing their opening four games without scoring.
Jack Rudoni’s penalty early in the first half put Coventry ahead with their first ever Premier League goal at the CBS Arena, which became their home in 2005.
Guinean forward Sidiki Cherif increased the Sky Blues’ lead after the interval.
Sven Botman got one back for Newcastle, but Ellis Simms and Stephen Mfuni struck late to ensure Coventry jumped from 19th to 14th place.
Lampard’s men had taken their first points of the season by beating Nottingham Forest 1-0 before the international break.
And Coventry’s first win over Newcastle since 1999 bolstered their bid to avoid relegation in their first season in the Premier League since 2001.
They will look to make it three consecutive wins when they travel to troubled Tottenham on October 19.
A win would have taken Newcastle into fourth place, but instead they were beaten for the second time in six league games this season.
Matthias Jaissle’s team were punished for squandering a host of chances in the first half.
Newcastle goalkeeper Lukas Hornicek handed Coventry a needless penalty in the sixth minute when he fumbled the ball and tripped Cherif in despairing bid to clear the danger.
Joe Willock teed up Harvey Barnes midway through the first half, finding space outside the Coventry area and picking out his Newcastle team-mate for a close-range effort that he flicked narrowly wide.
Newcastle monopolised possession and Jacob Murphy lashed just over from distance before Matias Fernandez-Pardo’s shot was cleared off the line by Bobby Thomas.
Having made one goal-line block to deny Fernandez-Pardo, Thomas did it again with another brilliant clearance on the stroke of half-time after the Newcastle forward rounded Carl Rushworth.
Coventry took full advantage of Thomas’s heroics to double their lead three minutes after half-time
Making his first Premier League start after joining from Fenerbahce in the summer, Cherif ensured it would be a day for him to remember forever as the 19-year-old smashed a fine finish into the bottom corner from the edge of the area.
Botman reduced the deficit in the 70th minute when the defender lashed a blistering blast past Rushworth from 20 yards.
But Newcastle midfielder Joelinton, making his first appearance of an injury-plagued season, was guilty of the decisive mistake in the 81st minute.
Joelinton’s heavy touch on the edge of his own area allowed Simms to pounce with his first touch after coming off the bench as the striker’s deflected drive whistled past Hornicek.
Mfuni, on loan from Manchester City, put the seal on Coventry’s vibrant display when he blasted home from long-range in the 86th minute. (AFP)
