Wanderers responded well to falling behind and deservedly levelled 16 minutes later, Tyrone Mears finding Alonso, who nodded home from close range.
The hosts completed the turnaround on 33 minutes courtesy of a brilliant piece of play between Kevin Davies and Lee.
Davies found Lee with a perfectly-weighted through ball and the South Korean international beat Jack Butland with a clinical finish.
Bolton were awarded a penalty kick 12 minutes from time when Steven Caldwell was penalised for handball.
Butland dived the correct way, but he was unable to stop Andrews converting the spot kick and notching his third goal in as many games.
Zigic's red card came with just three minutes remaining when he was shown a second yellow card for a clumsy tackle on Tim Ream.