Millwall could have added a fourth late in the game when Jack Smith sent a low ball across the penalty area, which John Marquis only just failed to get contact on.
Alexander, who replaced regular first-choice goalkeeper Allan McGregor as per the previous rounds of the competition, wanted too much time with a backpass and was almost caught by Jack Ross but the ball rebounded out for a goal-kick.
Craig Dargo volleyed over the bar after Diamond had failed to deal with Jack Ross's searching ball into the area as the Buddies enjoyed a rare period of sustained pressure.
However, the visitors were handed a lifeline late on when former Falkirk player Jack Ross was deemed to handle the ball on the line, and Arfield powered the penalty kick high into the net.
"Jack tried to clear the ball, it bobbled, Kerrea Gilbert was round to cover and so it was debatable if he was the last man, " Pearson added.
Coventry continued to press and looked like they would grab a deserved win when McSheffrey beat Jack Cork to a loose ball on the right flank, turned into the box to evade two more challenges and curled a delicate left-footed effort beyond Grant into the top corner.
It owed much to the hard work of Constable, who beat York keeper Michael Ingham to a long ball over the top, lofting it back into the middle where Jack Midson nodded down to Green who dispatched a sweet left-foot half-volley into the top corner from the edge of the box.
The only blot on City's day came when captain Vincent Kompany was sent off for a sliding two-footed tackle on Jack Wilshere, though the Belgium defender appeared to win the ball.
Louis Cardinals, with Robinson Cano in the Jack Clark role as the only guy around who can hit the ball out of the infield.
Currently, Gil Hodges and Jack Morris are both inextricably tied to the fact that only two ball players have ever eclipsed 60% in the Hall of Fame voting and were never elected to the Baseball Hall of Fame.
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Westwood was only able to parry Jack Colback's low drive, with Fallon on hand to fire the loose ball into the roof of the net.
Jack Morris lived by the mantra of being on the field at the end of a ball game to shake hands with his teammates after a victory.
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