And for the first time, winning teammates on the road.
Carr threw two touchdown passes in the first half and Woodson intercepted Josh McCown's pass with 38 seconds left, giving Oakland a 27-20 victory over the Cleveland Browns on Sunday and ending the Raiders' 11-game road losing streak.
It was the Raiders' first road win since Nov. 17, 2013, and Oakland also ended a 16-game slide in games played in the Eastern time zone.
''To go into someone else's place and get a win, it's probably one of the hardest things to do in the NFL,'' said Carr, who went 0-8 as a road rookie last season. ''I'm just happy for our team.''
Carr finished 20 of 32 for 314 yards and two touchdowns: a 3-yarder to Andre Holmes and 13-yarder to Seth Roberts. Latavius Murray ran for 139 yards and rookie wide receiver Amari Cooper had eight catches for 134 yards as the Raiders (2-1) held off a late McCown-led rally by the Browns (1-2) and went over .500 for the first time since the 2011 season.
First-year Oakland coach Jack Del Rio has been preaching to his players that this year can be different and not to dwell on the past. The Raiders are listening.
''This is what coach Del Rio has been talking about all offseason,'' Woodson said. ''We need to change the culture of football here. The last couple of years, we don't win these games. The last few weeks to pull out two tough games is really huge for this team.''
Last week, Carr shook off a late interception and led the Raiders to a comeback win at home over Baltimore. He was sharp from the outset against the Browns, helping the Raiders open a 27-10 lead before the Browns stormed back and closed within seven on McCown's 4-yard TD pass to Travis Benjamin with 6:28 left.
McCown, who heard chants for Johnny Manziel during his home debut, drove the Browns to Oakland's 35 in the final minute, but his pass to the right sideline for Benjamin was a tad late and Woodson picked it off at the 12 to save the Raiders.
''He never ceases to amaze me,'' Carr said of Woodson, in his 18th pro season. ''When he makes plays like that, it's kind of expected. I don't know if that's a good thing or a bad thing but we just kind of expect him to do that because that's Woody.''
Here are five other takeaways from Oakland's second straight win:
NO, JOHNNY, NO: McCown and Cleveland's offense started sluggishly, prompting some Cleveland fans to chant for Manziel, who guided the Browns to a win in their home opener last week.
Browns coach Mike Pettine said, ''No, none,'' when asked if he considered pulling McCown for Manziel.
''You can't put a player in a situation where he feels like he's playing with a short leash,'' Pettine said. ''We want our quarterback to play well. We have to play better around him.''
RARE ROOKIE: Cooper showed why he was the No. 4 overall pick with his second straight 100-yard game. He and Carr already have chemistry. The duo combined for 54 yards on Oakland's opening series and Carr connected with Cooper on a 40-yard pass to set up the Raiders' first TD.
''I like watching him after the catch,'' Carr said. ''He's a home run waiting to happen.''
HURTING HADEN: Browns Pro Bowl cornerback Joe Haden already had his hands full with Cooper and then sustained a rib injury on the game's first play.
With Cleveland's secondary missing starting nickel back K'Waun Williams, Haden pushed through the pain but left the field for X-rays. He returned and said he will undergo an MRI on Monday.
AGELESS WONDER: Woodson, who will turn 39 on Oct. 7, made his 61st career interception. He's made at least one in each season, one shy of the league mark held by Darrell Green, who made an interception in 19 consecutive seasons.
LINE OF FIRE: Cleveland's offensive line, touted as one of the league's best, has struggled so far this season. The Browns gave up five sacks and center Alex Mack committed a false start on 4th-and-goal at Oakland's 1, forcing the Browns to kick a field goal.
''I didn't snap the ball,'' Mack said. ''I didn't hear the cadence. It was basically offsides by me.''
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