Baltimore sacked Brandon Weeden five times, finally driving him out of the game with a thumb injury in the fourth quarter of a 14-6 victory on Sunday.
After yielding 49 points and 510 yards in a lopsided loss at Denver, Baltimore (1-1) kept Cleveland out of the end zone. The Ravens came into the game ranked last in the NFL in total defense.
"You have to have a short memory," said Terrell Suggs, who had six tackles and a sack. "We played really good on defense."
Cleveland has scored only one touchdown in its first two games under first-year coach Rob Chudzinski.
"We just have to keep grinding," Chudzinski said. "We have to keep working at it. The plays are there, the things are there. We're just off a little bit."
"After that game against Denver, we wanted to come back today and really show what we could do," tackle Haloti Ngata said.
Flacco went 22 for 33 for 211 yards. Just over an hour before kickoff, his wife gave birth to the couple's second child.
"Anytime you have a child, it's one of your best days," Flacco said. "The game didn't go exactly how we wanted it to, but that's how we've won football games around here. Sometimes you have to do it in an ugly way."
In the first half, Flacco was 2 for 6 for 9 yards on third down.
"I wasn't frustrated because I looked at Joe, and Joe wasn't frustrated," Brown said.
After halftime, Flacco went 7 for 8 for 87 yards on third down, getting six first downs in the process.
Weeden completed 21 of 33 passes for 227 yards before he hit his right thumb on a Baltimore helmet during the follow-through.
"I couldn't grip the ball, so I knew I had to come out," he said. "It really hurts. But the X-rays were negative."
"We had to take our time and be patient," Flacco said. "You know, it was only 6-0. No need to panic or get all crazy."
Limited to 122 yards in the first half, the Ravens moved 80 yards in 12 plays on their opening possession of the third quarter to take a 7-6 lead. Before Pierce scored, Flacco went 3 for 3, completing all three passes on third down.
Browns defensive tackle Phil Taylor shoved Rice in the facemask after the game's second play from scrimmage, turning a third-and-13 into a first down. But Tucker misfired to end the 12-play drive.
Cleveland's first offensive play was a 53-yard pass to Jordan Cameron, setting up Cundiff's first field goal.
The game's next eight possessions ended with punts. The trend turned just before halftime, when a 27-yard completion from Flacco to Torrey Smith led to another missed field goal try by Tucker.
Cleveland then moved 33 yards before Cundiff connected with 11 seconds left.
The second half, however, belonged to Baltimore. The Browns made only five first downs after halftime and finished 4 for 15 on third downs.
"We had a great camp, a great preseason," wide receiver Davone Bess said. "We're just not making the necessary plays. Third down, we've got to be able to own that down, and be able to execute in the critical moments of the game."
NOTES:Ravens DL Chris Canty sustained a groin injury. ... Browns LB Quentin Groves sprained his ankle. X-rays were negative. ... Ravens CB Chykie Brown strained his knee. ... DE Paul Kruger, who left Baltimore to sign as a free agent with Cleveland during the offseason, had three tackles and no sacks.
Copyright 2013 by The Associated Press