However, Alex McLeish's men are struggling in the league and their team selection for this match - which had only two survivors from Wednesday's starting XI - was a testimony to their priorities for the rest of season.
That said, McLeish is able to call upon some quality replacements for some of his front-line forces. Phillips rolled back the years with a superb display, which was capped by the decisive strike with 17 minutes left to play.
The 37-year-old had seen a header tipped onto the bar by Keiren Westwood in the opening minutes of the game but the Coventry keeper was powerless to prevent the forward's crisply struck volleyed winner after Jean Beausejour's corner had picked out the striker.
Such a finish to the game seemed unlikely midway through the first half, when Wood's towering header from a Gary McSheffrey corner had added to King's finely-struck low finish to give Coventry a 2-0 lead.
Coventry's confidence was shaken, though, by Bentley's timely 25-yard strike - which found the net via the underside of the bar - in the 35th minute, the midfielder's first for the club since
joining on loan
from Tottenham just over two weeks ago.
Birmingham were much-improved after the break and deservedly drew level through Parnaby, who hooked into an empty net for his first Birmingham goal after Hleb had drawn Westwood and pulled the ball back.
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