Quarterback Jimmy Garoppolo did not miss a beat as he stepped in for the suspended Tom Brady in his first NFL start and led the New England Patriots to a 23-21 win over the Arizona Cardinals.
Garoppolo threw for 264 yards and a touchdown but it was a missed 47-yard field goal with 41 seconds remaining from Arizona's Chandler Catanzaro that enabled the Patriots to hold on for victory.
Garappolo completed 24 of his 33 passes with no interceptions, while Arizona's Carson Palmer threw for 271 yards and two touchdowns, both to Larry Fitzgerald.
The Patriots were without Brady, suspended for his role in "deflategate", tight end Rob Gronkowski and Rob Ninkovich, but scored touchdowns from Chris Hogan and LeGarrette Blount.
Kicker Wil Lutz missed a 61-yard field goal attempt in the dying seconds as the New Orleans Saints were beaten 35-34 by the Oakland Raiders.
The Raiders scored 22 points in the fourth quarter, edging in front with Michael Crabtree's two-point conversion, and although the Saints made good progress upfield, rookie kicker Lutz put his game-winning attempt wide of the left-hand upright.
Joe Flacco and Mike Wallace combined for a 66-yard touchdown as the Baltimore Ravens battled to a 13-7 win against the Buffalo Bills, while a stunning 54-yard touchdown from the impressive AJ Green helped the Cincinnati Bengals to a narrow 23-22 success against the New York Jets.
The Chicago Bears slipped to a 23-14 defeat to the Houston Texans in their opener, with rookie Will Fuller's fourth-quarter touchdown proving decisive.
A stunning touchdown catch from Austin Sefarian-Jenkins helped the Tampa Bay Buccaneers to a 31-24 win over the Atlanta Falcons, while the Green Bay Packers held on for a 27-23 win against the Jacksonville Jaguars, with Jordy Nelson scoring a rare touchdown.
Russell Wilson threw a two-yard touchdown pass to Doug Baldwin with 31 seconds remaining to give the Seattle Seahawks a 12-10 win over the Miami Dolphins and Eli Manning threw for three touchdowns to help the New York Giants beat the Dallas Cowboys 20-19.
Matt Prater atoned for an earlier miss with a 43-yard field goal with eight seconds remaining to edge the Detroit Lions to a wild 39-35 win over the Indianapolis Colts.
Robert Griffin III endured a miserable debut for the Cleveland Browns as the Philadelphia Eagles ran out 29-10 victors.
A snap went over the quarterback's head and into the end zone to gift the Eagles two points, with Griffin's counterpart Carson Wentz impressing with touchdown passes to Jordan Matthews and Nelson Agholor.
The Minnesota Vikings recovered from a scoreless first half to claim a 25-16 victory against the Tennessee Titans, with Eric Kendricks' 77-yard interception return the pick of the scores.
The Kansas City Chiefs produced the largest second-half comeback in franchise history as they claimed a 33-27 overtime win against the San Diego Chargers.
The Chiefs were 24-10 down going into the fourth quarter, but touchdowns from Jeremy Maclin and Spencer Ware helped to force overtime.
Quarterback Alex Smith took matters into his own hands to run in the winning score for the home side.
Earlier, Melvin Gordon had put the Chargers in control with the first touchdowns of his NFL career.
Big things were expected of running back Gordon when he was selected 15th overall in the 2015 draft, but he failed to score once during his rookie season.
His first NFL touchdown arrived in the first quarter from a yard out, but Gordon then followed that in the second with a six-yard run, but it was all to no avail.
Kansas City Chiefs players locked arms as a "sign of solidarity" during the American national anthem on Sunday night, but cornerback Marcus Peters raised a fist to show support for protests started by San Francisco 49ers quarterback Colin Kaepernick.
The anthems took on more significance on the 15th anniversary of the September 11 attacks in the country, but Peters' was the only visible gesture in the early games, adding to Brandon Marshall's decision to kneel on Thursday evening.
Before the game, the Chiefs released a statement which read: "After having a number of thoughtful discussions as a group regarding our representation during the national anthem, we decided collectively to lock arms as a sign of solidarity.
"It was our goal to be unified as a team and to be respectful of everyone's opinions, and the remembrance of 9/11.
"It's our job as professional athletes to make a positive impact on our communities and to be proactive when change is needed.
"Together we are going to continue to have conversations, educate ourselves and others on social issues and work with local law enforcement officials and leaders to make an impact on the Kansas City community."
But Peters was keen to give his backing to Kaepernick, who was the first to refuse to stand for the national anthem in pre-season games in a stance against perceived racial injustice.
Kaepernick's 49ers team-mate Eric Reid and Seattle Seahawks cornerback Jeremy Lane also staged similar demonstrations.
On Sunday the Seahawks were playing the Dolphins, who had four players take a knee during the national anthem before the game - Kenny Stills, Michael Thomas, Arian Foster and Jelani Jenkins.
The Seahawks players locked arms on the opposite side of the field.
In the late game, New England Patriots' Martellus Bennett and Devin McCourty held up their right arms, while team-mate Danny Amedola grabbed hold of the large unfurled American flag on the field during the anthem.
