I don't have any stats to prove or disprove any theories, but I do think it has more to do with matchups and timing than anything else. When we played Denver, we were coming off 2 wins that didn't show any chemistry between Tom and his new receivers who probably were still trying to learn the NE playbook plus routes, etc. Then you have Denver's great run defense which was able to stuff Maroney while Dillon was semi-inactive after a few plays and the Pats were forced to rely totally on Tom and the air attack. Champ Bailey is widely known as a shutdown corner so your option throwing anywhere near him is dangerous(last year for example), so all Denver had to do was contain Brady and play zone and NE is essentially neutralized whether or not you have a great gameplan.
Coming off that loss, Tom and his receivers got another week to work out their timing and routes, the vets probably rejuvenated the team because they ARE Patriots and Patriots don't lay down and die, and everyone outside the team thought they were going to lose and it may have sparked something . Then you have the Bengals bad run D, Chris Henry disrupting some of the gameplans Marvin probably wanted to utilize, and Tom probably pissed at everyone talking about his goddamn body language, it all adds up.