The big forward pounced on a poor pass early in the match and earned a win against a side reeling from the sale of its captain.
Bunbury's goal came just 20 minutes into the match and the Revs failed to recover.
Dimitry Imbongo had maybe the best chance to pull New England level just after the break. Chris Tierney's whipped cross found the forward open in front of goal.
Fernando Cardenas had a nice chance of his own just minutes later, storming forward and blasting his shot wide of the target. Late on Tierney had a shot at goal take a deflection, but Jimmy Nielsen reacted well preserved the win for Sporting.
Earlier in the week New England dealt captain Shalrie Joseph to Chivas USA.
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