Joachim's miss on 66 minutes was even worse than Ryan Giggs' recent effort against Arsenal.
The striker had looked impressive after scoring in midweek, but after rounding the keeper and with the goal at his mercy, Joachim skied the ball over from 12 yards.
But he made up for it with a cool finish after 74 minutes when he latched onto a Dean Holdsworth downward header and slotted past Kelvin Davis.
Earlier, Wimbledon came close to opening the scoring after just three minutes when Gareth Ainsworth's attempted cross dropped onto the crossbar.
But they did take the lead ten minutes later, when David Connolly was given far too much time and space on the edge of the box.
Four City defenders surrounded him yet none made a challenge as he picked his spot effortlessly in the bottom left corner.
The goal brought Coventry to life and they dominated for seven minutes until they forced an equaliser.
A Gary McAllister corner found John Eustace who rose to head emphatically into the back of the net for his second goal since returning from a loan spell at Middlesbrough.
Connolly could have added a second on 37 minutes after he skipped past challenges from Mo Konjic and Andrew Whing, but Morten Hyldgaard came off his line to make an excellent block.
Wimbledon had a reasonable penalty shout when Ainsworth went down under a challenge from Youssef Chippo on 52 minutes.
But they sealed a draw when captain Neil Shipperley raced into the box to stab home Patrick Agyemang's excellent low cross on 76 minutes, before McSheffrey was dismissed for a second bookable offence in injury time.