FOXBOROUGH — Early in the fourth quarter of the Patriots’ 34-16 win over the Texans, safety Duron Harmon told defensive backs Devin McCourty and Logan Ryan that if he didn’t get an interception before the end of the game, he wasn’t going to be able to sleep later that night.

It wasn’t that the Patriots, holding onto a comfortable two-touchdown lead, desperately needed another turnover. It was that McCourty and Ryan already had interceptions of their own, meaning two of the three Rutgers alums on the roster had forced a turnover. Harmon, the other former Scarlett Knight, wasn’t going to be left out of the party.

With the game winding down and the Texans driving, Harmon got his wish. Houston quarterback Brock Osweiler tried to lead a comeback and instead sailed a pass that landed right into Harmon’s chest to complete the Rutgers trifecta.

“That’s a Rutgers night,’’ Ryan said. “Bill [Belichick] gave us a shout-out, so if you’re a DB, come to Piscataway [N.J.].’’

Added Harmon: “[Belichick’s] probably going to have some other words to shout at us in our meetings, but I’ll take it for right now.’’

In a season highlighted by a defense that cedes yards (326 yards per game, 8th in the NFL) but not points (15.6, 1st), Saturday was no exception. The Texans scored a season-high 13 points off turnovers, the most allowed by the Patriots in a playoff game since the 2009 wild-card round, but that number is directly related to the fortuitous field position gifted by the Patriots’ offense and one that could’ve been a lot higher.

Three times, the Patriots turned the ball over to the Texans inside their own 35-yard line. Twice, New England forced a field goal. The only touchdown given up by the defense came when Dion Lewis fumbled a kickoff to give Houston the ball at the 12-yard line in the second quarter. After giving up 13 points in the first half, the Texans would score just three more the rest of the way, and Osweiler threw all three of his interceptions in the second half.

“We were angry at ourselves,’’ McCourty said. “So going into halftime, we just looked at each other and said, ‘We got to play better. Do what we’re supposed to do and make them earn it.’ We did a much better job of that.’’

The New England secondary seemed to take particular pride in Ryan’s interception, which came early in the fourth quarter with the Texans down a touchdown, because they saw it coming. Before the play, McCourty recognized the formation and told Ryan to play underneath wide receiver DeAndre Hopkins instead of over the top. Osweiler tried to force a pass, and Ryan, in perfect position, jumped the route and returned the interception 23 yards. Two plays later, Lewis shoved his way into the end zone and effectively sealed the game, 31-16.

“We actually talked about the play before it happened, which is crazy,’’ Ryan said. “That’s something with film study and preparation we were able to talk about and make plays. They ran exactly what we thought they would and we capitalized.’’

All night, the Patriots were able to shut down the Texans’ playmakers. Osweiler threw for 198 yards and averaged under five yards per throw. Running back Lamar Miller ran for 73 yards on 3.8 yards per carry. Hopkins caught six passes for 65 yards.

Ryan had one of his best games of the season. Along with the interception, he led the team with three passes defended and recorded seven tackles and a sack.

“I felt like I played terrible in the division game last year against Kansas City, so I felt like this was some redemption,’’ Ryan said. “I felt comfortable playing against this offense, I’ve seen Hopkins for years, and had a pretty good game against them the first time.

“I knew they were going to come after me, so I just wanted to be extra locked in and be able to capitalize so when they were throwing at me I didn’t want to let the team down.’’

Everett Cook can be reached at evcook4@gmail.com.