At least this one was much closer than last week's 49-20 embarrassment to the Philadelphia Eagles. But no less frustrating.
"It was very winnable," said Pryor, 11 for 26 for 122 yards. "We're close. But we got a blocked punt and an interception they took down to the 4. You can't win like that. We've got to learn."
Allen said his team was focused and determined to win a game after last week's rout.
But they struggled at key times, especially settling for the 24-yard Sebastian Janikowski field goal and a 20-14 lead when they could have been up 10 points.
Rashad Jennings had an opening run on first-and-goal, but it closed quickly. Pryor threw an incompletion on the next two downs, the last one from the 6 after a procedure penalty against tackle Khalif Barnes.
"It's frustrating," said Jennings, who had 88 yards on 20 carries. "You want to think you can punch it in. We've got a physical bunch of players up front, so there's no excuses, starting with myself, not to get it into the zone.
The error-prone Giants (3-6) handed the Raiders their first 17 points on first-half turnovers. But they got 115 yards rushing by Brown in his first game of the season, and another big defensive game to keep their season alive.
The Raiders had just 213 yards of total offense.
Despite that, Tracy Porter's interception return for a touchdown off Eli Manning put the Raiders ahead 17-14 at the half. Janikowski's field goal capped the 14-play, eight-minute drive early in the third quarter.
It should have been more, though. And it cost the Raiders dearly.
Oakland got the ball back at the New York 48 following a 27-yard punt by Steve Weatherford into a stiff breeze.
But Thomas, who missed the past two seasons with ACL injuries, made the biggest play of the game. He stepped in front of Denarius Moore and sped toward the end zone, avoiding a tackle by Pryor inside the 20 before being tackled by Andre Holmes.
"He made a good play," Pryor said. "They were in cover-2 and he faked like he was going inside. I threw outside, and he went out and made a great play. I saw him tuck in and he gave me a fake. He did a good job."
Brown, who broke his left leg for the second time in less than a year in the preseason finale, gave the Giants the lead from the 1-yard line following a pass interference call.
Josh Brown added a 23-yard field goal in the fourth quarter and New York clinched the game when Mathias Kiwanuka had a sack and a forced fumble on Oakland's final possession.
"We don't make it easy on ourselves, but we find a way to win," Giants coach Tom Coughlin said. "The only way that happened is, the players at halftime believed they were going to win."
The victory kept them alive in the NFC East race.