The Gunners were in firm control of possession throughout, but the first half ended goalless despite a number of shots for the home side.
Arsenal's captain Robin van Persie ended the dearth of goals a little over 30 seconds into the second half, netting from inside the area with help from Aaron Ramsey.
The Reds' advantage was bolstered a few minutes later as the Trotters' David Wheater was sent off after an unfair challenge on Theo Walcott.
Van Persie increased his side's chances 20 minutes from the end with a low strike, hitting a personal milestone of 100 goals for the club.
While Zat Knight frustrated Van Persie's attempt at a hat-trick ten minutes later, Alex Song went on to make it three at 89 minutes.
Bolton are now holding up the table with three points from six games, while Arsenal move from 17th place to 12 with seven points in total.