The Sky Blues gave Black the job on a permanent basis after previous boss Gary McAllister decided to leave his position to take care of his sick wife.
Andy Morrell started the scoring when he headed home a Stephen Warnock corner in the sixth minute for his first goal since October.
The hosts were not helped when Stefan Oakes was dismissed for a lunge on Andy Whing that forced referee Lee Mason to show the midfielder a straight red.
The official did not make himself popular with the home crowd when he appeared to deny Walsall a penalty when Callum Davenport climbed all over Gary Birch inside the box.
The Saddlers did manage to level matters just before the break when Darren Wrack slotted home with a sweet side-footed effort.
Parity did not last long after half-time though as Gary McSheffrey cut in from the right and rifled in from 20 yards out to put the visitors back in front.
Morrell netted his second from close range to make it 3-1 on 57 minutes and Julian Joachim made the points safe when he broke away to score a fourth for Coventry.
Walsall did not make life easy for themselves as Ian Roper's own goal made it five and The Sky Blues were flying high when McSheffery completed the scoring with ten minutes to go.
The striker did waste a glorious chance to claim a hat-trick when he missed a penalty with five minutes to go but it did not take the shine off a tremendous afternoon for Coventry and their new man in charge.
