James Forrest and Jim McAlister were both sent off earlier in the game and Mensing joined them when he conceded the last-gasp spot-kick as the points were shared. Freddie Ljungberg was dropped to the bench.
Hamilton went ahead in the 28th minutewhen Simon Mensing pounced to nod home. Martin Canning appeared to be in an offside position but the goal was allowed to stand.
With half-time approaching, irate Celtic boss Neil Lennon – in the spotlight after picking up a six-match touchline ban starting next week — earned himself a lecture from referee Willie Collum.
Celtic suffered another setback four minutes after the restart when Forrest dived in late with a rash challenge on David Buchanan and was shown a straight red card.
Accies threw McAlister into the action in place of McLaughlin after 62 minutes but he was sent off after just 35 seconds on the field following a reckless tackle on Mark Wilson, who was replaced by Niall McGinn moments later.
Just when Accies thought they had held on for the win, the referee pointed to the penalty spot in the last minute, as Mensing was sent off for a foul on Emilio Izaguirre in the box. Stokes stepped up to send the goalkeeper the wrong way with the spot-kick.
HAMILTON: Cerny, McLaughlin (McAlister 62), Graham, Canning, Mensing, Flavio Paixao, Buchanan, Gillespie (Wilkie 83), Skelton, Imrie, Hasselbaink (Casalinuovo 82).
CELTIC: Forster, Wilson (McGinn 66), Rogne, Majstorovic, Izaguirre, Forrest, Kayal (Brown 59), Ledley (Ljungberg 75), Mulgrew, McCourt, Stokes.
Referee: W Collum.
Result: Dundee Utd 2 Motherwell 0.