Andy Dalton missed a good chance to claim the first score of the match when the Bengals made a rare first-half visit to the opposition red zone, only for his pass to be intercepted.
The Bengals did eventually break the deadlock in a very tight first half, however, with Mike Nugent hitting a 39-yard field goal with 3:17 left of the second quarter.
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The Patriots made it 3-3 going into the break through Stephen Gostkowski's 42-yard kick, but Nugent restored the hosts' lead with a 50-yard field goal in the third quarter.
The first touchdown of the match finally came in the fourth quarter as the Bengals took a firm lead in the match for the first time through BenJarvus Green-Ellis's one-yard run.
Gostkowski struck another field goal for the Patriots in the final quarter to bring them within a touchdown of the Bengals, but it wasn't enough as Cincinnati held out to maintain their 100% home record this season.