BALTIMORE -- Eight yards deep in the end zone when he caught the kickoff, Jacoby Jones had an instant to decide: Take a knee or run.
He ran -- all the way into the record book.
"You know when you get that itch? I wanted to scratch it," Jones said. "So I took it."
The Cowboys amassed 481 yards against a crippled Baltimore defense and held the ball for more than 40 minutes. Dallas totaled 227 yards rushing, the most against the Ravens since the franchise arrived in Baltimore in 1996.
It wasn't enough. Jones' return put the Ravens (5-1) ahead 24-13 in the third quarter, and Dallas (2-3) never got even against a defense that lost cornerbacks Lardarius Webb (right knee) and Jimmy Smith (lower leg strain), along with middle linebacker Ray Lewis (triceps) and defensive tackle Haloti Ngata (knee).
Webb tore his ACL, a league source told ESPN NFL Insider Adam Schefter.
Lewis will have an MRI on his triceps Monday, a team source confirmed to ESPN's Ed Werder.
And Ngata sprained his MCL and will have an MRI on Monday, a league source told Schefter.
"They threw a lot of haymakers at us," Harbaugh said. "Our guys stepped up at the end and found a way to win the game."
After Dez Bryant scored on a 4-yard pass from Tony Romo with 32 seconds left to make it 31-29, the 2-point conversion pass zipped through the arms of the diving Bryant in the front left corner of the end zone.
Dallas recovered the onside kick, but Dan Bailey was wide left on a 51-yard field goal try with 6 seconds remaining.
"I felt we fought really hard and well through a lot of different adversities in all three phases," Cowboys coach Jason Garrett said. "(The Ravens) have been awfully good for a while. This team's been awfully good in this place for a while. We gave them everything they could handle."
Ray Rice scored two touchdowns and Joe Flacco threw for a score to help the Ravens secure their fourth consecutive victory and enhance their grip on first place in the AFC North. Baltimore's home winning streak is the longest current run in the NFL.
"To set the National Football League record for a kickoff return, in what was the difference in the game, is pretty special," Harbaugh said.
The score was essential to the Ravens, who mustered only 1 yard on three offensive plays in the third quarter.
After Jones' touchdown, the Cowboys launched an 80-yard march that ate up more than eight minutes. Romo connected with Bryant for 13 yards on a third-and-11 before throwing a 7-yard touchdown pass to Bryant to make it 24-20.
Dallas followed with two strong defensive series, and a short punt by Baltimore preceded a 21-yard drive to a field goal by Bailey.
Flacco then directed a 10-play, 73-yard march. A 31-yard completion to Anquan Boldin moved the ball to the Dallas 4, and Rice scored from the 1 to provide the Ravens an eight-point cushion.
The Cowboys rallied, but could not complete the comeback.
"At the end of the day, we've got to finish the game and we have to win the game," Garrett said. "We didn't do that."
Added Dallas tight end Jason Witten: "Obviously they're a good team and you don't walk away saying, 'Hey we played a good team close.' You walk away saying, 'We had an opportunity and we lost.' "
Romo went 25 for 36 for 261 yards and two touchdowns, a redemptive performance after he threw five interceptions in his last outing against Chicago. DeMarco Murray ran for 93 yards, Felix Jones had 92 on the ground and Bryant caught 13 passes for 95 yards and two TDs.
Murray left in the second half with a foot injury. His absence did little to deter the Cowboys' running game.
"We ran it inside, we ran it outside, we got some stuff off the run game," Garrett said. "We kept the ball for a long time and those were all good things."
Baltimore trailed 10-3 before scoring touchdowns on a pair of 80-yard drives to take a 17-10 halftime lead.
The Ravens pulled even when Rice ran in from the 1 after a hands-to-the-face penalty against Dallas lineman Kenyon Coleman on third-and-goal from the 2. Earlier in the march, Rice ran 43 yards with a short pass.
Cary Williams' third interception in three games gave the ball back to Baltimore. Flacco completed two 20-yard passes to Boldin before hitting Torrey Smith for a 19-yard score with 41 seconds left in the half.
Facing the top-ranked pass defense in the NFL, Flacco went 13 for 18 for 174 yards in the first half.
The Ravens opened the game with a 14-play drive that lasted over seven minutes and ended with a 38-yard field goal.
Dallas answered with an 80-yard march culminated by a 22-yard run by Felix Jones and featuring a 28-yard run by Murray, longest against the Ravens since 2010. The Cowboys' next possession stretched more than six minutes, covered 56 yards and produced a 42-yard field goal by Bailey for a 10-3 lead.
Ravens C Matt Birk played in his 200th NFL game. ... Bobbie Williams started at guard for the Ravens in place of Ramon Harewood, who was inactive after five straight starts. . Baltimore Orioles manager Buck Showalter accompanied the Ravens captains to the coin toss and received a standing ovation. ... Cowboys DL Sean Lissemore left in the first quarter with an ankle injury.
Information from ESPN's Ed Werder, ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.