Mayfield threw two touchdowns in two-plus quarters and Barkley ripped off a dazzling 39-yard run on the opening play from scrimmage as the Browns beat the Giants 20-10 on Thursday night.
"I'm aware that it was the first game and in that respect, it's not so bad," Mayfield said after showing why the Browns made him the top pick.
Replacing starting quarterback Tyrod Taylor late in the first quarter, Mayfield hit 11 of 20 passes for 212 yards, didn't turn the ball over and converted two fourth-down plays with his feet.
"I thought he did some good things out there," Cleveland coach Hue Jackson said. "I'm honestly not surprised by anything Baker does. This was his first opportunity and he'll grow from it."
The Heisman Trophy winner from Oklahoma found tight end David Njoku on a 10-yard TD pass to cap a 14-play, 72-yard drive on his second series. He finished his debut with a completion on a 54-yard slant and run to fellow rookie Antonio Callaway .
Taylor, expected to be coach Jackson's starter as Mayfield learns this season, hit all five of his passes in two series, including a 36-yard touchdown pass to Njoku , a New Jersey native.
Barkley electrified the fans at MetLife Stadium, taking a handoff from Eli Manning on his first NFL touch and turning on the jets on a 39-yard jaunt down the sideline in front of the Giants' bench. It set up a 42-yard field goal by Aldrick Rosas.
"I loved his first run," Giants coach Pat Shurmur said of the Penn State halfback. "If only they all could be like that. You could see, it wasn't too big for him."
Barkley scoffed at the idea he made something out of nothing on the play. There was a hole, he said.
"Everybody talks about the speed difference in the NFL, but to see you still have that burst and you can get to that line of scrimmage like that and create space; I just have to find a way to gain even more yards than that," said Barkley, who finished with 43 yards on five carries.
Manning played two series and hit 4 of 7 passes for 26 yards. Star receiver Odell Beckham Jr., returning from major ankle surgery, dressed but was held out by Pat Shurmur, who is trying to rebuild the Giants after a 3-13 season.
The Browns went 0-16 last season after winning their four preseason games.
CALLAWAY: The troubled fourth-round pick played despite being cited for marijuana possession and driving with a suspended license. Police also found bullets and a gun part in his car this week. He had three catches for 87 yards, including a diving 24-yarder that the Browns successfully challenged after it was ruled incomplete on the field.
DEZ BRYANT: -- The Browns have had interest in free agent receiver Dez Bryant, and the former Cowboy tweeted during the game he was coming to visit GM John Dorsey. The Browns may not need him. Free agent signee Jarvis Landry had two catches for 36 yards in very limited action. Callaway added 87 yards and third-year pro Rashard Higgins looked good with four receptions for 66 yards.
GIANTS WOES: This looked a lot like the Giants of last year. Except for the opening play, the offensive line struggled, particularly protecting the quarterbacks, although the run game generated 134 yards on 23 carries. ... The new 3-4 defense stopped the run but gave up too many big passing plays. ... Second-string QB Davis Webb struggled, going 9 of 22 for 70 yards. "He was a little too amped," Shurmur said.
Browns: Host Buffalo Bills on Aug. 16.
Giants: At Detroit Lions on Aug. 16.
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