United - nine goals in their last two home games - remain unbeaten at St James' Park and hold a three-point lead over West Brom and are five clear of third-placed Nottingham Forest.
The win means that Newcastle are now just 20 points behind the 83 points that gained Birmingham automatic promotion last season and still have a further 15 games to play.
After Clinton Morrison had put Coventry in front, Wayne Routledge levelled it up and Andy Carroll, Peter Lovenkrands from the penalty spot and substitute Ryan Taylor made it safe in the second half as Coventry had Leon Barnett send off for two bookings.
Coventry - unbeaten in five and on the back of successive wins - were the better side in the opening half, the only shock being it took the Sky Blues 35 minutes to break the deadlock.
Morrison's determined running posed plenty of problems and it was the former Republic of Ireland striker who swept in Carl Baker's left-wing cross.
Coventry's celebrations lasted only two minutes, with United level with a stunning Routledge volley - his first goal for United.
A short corner was played to the back post where Coventry skipper Stephen Wright got in a decent clearance, which was lashed low into the net by Routledge from 25 yards.
Earlier Kevin Nolan had popped up on the line to deny Morrison, while at the other end Keiren Westwood's stunning save saw him claw out a Lovenkrands header.
It took just eight minutes of the second half for Newcastle to go ahead when a good run from Jonas Gutierrez ended with Lovenkrands crossing and Carroll headed in to make it four goals in as many games and take his season's tally to double figures.
The issue was put beyond doubt after 69 minutes when Routledge was hauled back in the box by Barnett, who saw red after a second yellow card. Lovenkrands fired the resulting penalty high into the net to make it 3-1 and nine for the season.
It was one-way traffic after that and Newcastle had enough chances to have doubled their tally, but had to settle for just one more with substitute Taylor scoring in the final minute.