The New England Patriots’ pursuit of perfection produced more boffo ratings Saturday night, as the team’s final regular-season contest scored nifty Nielsens on a trio of networks.

Unprecedented simulcast on the NFL Network, CBS and NBC averaged 34.5 million viewers, according to preliminary Nielsen estimates — the largest aud for any telecast this season. Three previous Patriots games on CBS this season had averaged 29 million viewers or more, while the most-watched entertainment telecast is the season premiere of the Eye’s crime drama “CSI” (25.4 million).

Pats game was the most-watched NFL regular-season contest since a Dallas-Kansas City match-up on Thanksgiving Day drew 35.7 million viewers on NBC in 1995.

Individual network breakouts were not available, but it’s likely that CBS — which airs more Patriots games than any other network — had an edge over NBC. The league invited both broadcast nets to carry the potentially historic game because the NFL Network is available in less than half of the country’s homes.

Game also aired on a fourth outlet in the local markets of New York (WWOR) and Boston (WCVB).

The Patriots, which outlasted the Giants 38-35 to become the first team in 35 years to finish the regular season undefeated, will be back in primetime for their first playoff game — against an opponent yet to be determined — a week from Saturday on CBS.

The playoffs open this weekend with two games Saturday on NBC and one game apiece Sunday on Fox and on CBS. Fox will air the Super Bowl on Feb. 3.