Feagles broke the record when he kicked a 39-yard punt with 7:35 left in the first quarter. Referee Larry Nemmers gave Feagles the ball and shook his hand, and the two posed for a picture.
The record of 282 was previously held by defensive lineman Jim Marshall, who played from 1960-79 with the Browns and Vikings.
Feagles, 39, has not missed a game in his 18-year career, playing for New England, Philadelphia, Arizona, Seattle and the Giants.
Feagles almost missed games last season and in 1999. Against the Eagles last year, Feagles was hit on a punt return by Philadelphia's Jeremiah Trotter, causing a concussion. Coach Tom Coughlin said earlier this week he never thought Feagles would miss the Giants' next game.
"He's a tough guy and I never really considered that," Coughlin said.
With Seattle in 1999, Feagles broke his arm against Pittsburgh but had an extra week to heal because Seattle had a bye. He also injured his shoulder in 2002 against Philadelphia after a hit from N.D. Kalu but played the next week against Atlanta.
The try came at the end of the Cardinals' first possession with 10:38 left in the first quarter against Jacksonville.
Rackers' streak of 31 ties Fuad Reveiz (1994-95) for third-longest in NFL history.
Six of Rackers' kicks were beyond 50 yards. None of the other top five had more than two 50-plus kicks during their streaks.
Nedney was replaced in the lineup by Jose Cortez, a former 49ers kicker who was signed Friday. Cortez had been released by Philadelphia on Tuesday.
The nine-year veteran was released by the Titans in February in a salary cap move. In San Francisco he has 67 points, including 43 consecutive points that were the most by one player in the NFL since Matt Stover had 49 in a row for the 2000 Ravens.
An All-Pro last year after collecting 11½ sacks in his second NFL season, Williams had offseason surgery on his right knee. That hurt his conditioning, and Williams came to training camp overweight. He has only one sack this year.
The team said Herndon would not return.
Herndon appeared to be injured with 1:14 left in the first half. On second-and-goal at the Seattle 7, Herndon nearly intercepted New York quarterback Eli Manning's pass when he collided with the Giants' Tim Carter and was slow to get up.
In his first year with Seattle, Herndon was second on the team entering Sunday's game with 52 tackles. He's played in all 11 games and made his sixth start of the season on Sunday.
Tennessee Titans: Rookie receiver Brandon Jones sprained his right knee and went down to the grass as he was trying to turn back for a pass just before halftime. X-rays were negative, but coach Jeff Fisher said they will do more tests.
San Francisco cornerback Shawntae Spencer picked off the pass intended for Jones and ran 61 yards for a touchdown with 27 seconds left in the second quarter.
"I didn't see him go down," Titans quarterback Steve McNair said. "I threw it and got tackled, so I didn't know exactly what was going on until I rolled over and saw the guy going down the sideline. It was a scary moment for everybody I think. I hope he's going to be OK."
Jones, a third-round pick out of Oklahoma, has started eight games this season. He had sprained the same knee Oct. 23 in a loss at Arizona and missed a game.
He was able to walk off by himself but went straight to the locker room. He was not on the sideline at the start of the third quarter, and a team spokesman said Jones sprained his right knee. He did not return.