Coventry put up a brave effort throughout but the Magpies' quality in the final third proved the difference again in the 81st minute as substitute Nile Ranger grabbed his first professional goal.
It was not a classic at the Ricoh Arena but it was a game which proved Newcastle will take some stopping in their attempts to secure automatic promotion, this their seventh consecutive victory.
It also matched the club's best winning run since Kevin Keegan guided them to seven successive Premier League triumphs in 1996.
There was plenty of reasons to be optimistic for Coventry but the table does not lie, and their 10-match winless streak leaves them struggling at the wrong end of the table.
The big news prior to kick-off was Chris Hughton's decision not to include England Under-21 striker Andy Carroll in his matchday 18, just days after he was released on police bail having been questioned over an allegation of assault at a Newcastle night spot.
But for all the controversy off the pitch there was very little on it in the opening quarter, with neither keeper forced into a save and both sides battling for midfield supremacy.
The first chance of the encounter finally came midway through the half as Magpies left-back Jose Enrique saw his strike deflected narrowly wide.
Coventry could consider themselves fortunate on the half-hour mark as centre-back Leon Barnett appeared to pull back Peter Lovenkrands just outside the area when clean through.
However referee Grant Hegley, who was in a good position, wasted no time waving away the Dane's protests. The hosts were then more than unlucky themselves not to go ahead after 38 minutes.
Michael McIndoe back-heeled the ball to Leon Best in space on the left side of the penalty area and he rifled a shot that beat Steve Harper but cannoned off the bar.
The ball then fell back to Freddy Eastwood who crossed for McIndoe whose header clipped the bar for a second time in a matter of seconds.
But with a goalless interval approaching, Ameobi received the ball 12 yards out, turned Barnett and lashed a shot past Keiren Westwood.
The strike was somewhat harsh on Coventry with neither side having deserved to go behind after an even opening 45 minutes.
Best struck a well-taken volley straight at Harper 10 minutes after the restart as the home side went about their reply in a way which would have pleased manager Chris Coleman.
Westwood did well to get down to Alan Smith's effort at the other end before Harper was again called into action to keep out strikes from Eastwood and Aron Gunnarsson as the game opened up.
Another goal was looking likely as the game approached the final 15 minutes and Newcastle forward Ranger was only denied by some last-ditch defending from the hosts. But he got his goal with nine minutes remaining, converting from close range after a great run and cross on the left from Enrique.