Bradshaw and Cruz became the first tandem to rush for 200 yards and catch three TD passes in a game since 1960, when the Cardinals' John David Crow ran for 203 yards and Sonny Randle had three touchdowns receiving.
The Giants are 9-0 in games he has rushed for 100 yards or more. They rushed for 243 yards.
"I love this game more than anybody," Bradshaw said. "I put all my heart into it and I just feel I'm one of the toughest out there on the field."
New York also forced three turnovers, including Chase Blackburn's interception in the end zone midway in the fourth quarter to clinch it. That led to rookie David Wilson's first NFL touchdown, a 40-yard scamper, which Wilson celebrated with a flip in the end zone.
Weeden, Cleveland's other first-round pick, hit Gordon, on two touchdown passes. But the Browns wound up with 10 penalties for 91 yards.
"We started out fast and got an early lead," coach Pat Shurmur said. "We had a three-minute stretch before the end of the first half that was, 'Wow, you can't do that against a good football team.' "
Giants coach Tom Coughlin tied Bill Parcells for regular-season coaching victories with the franchise, 77.
Cruz, Randle and Dominek Hixon stepped up nicely with Hakeem Nicks and Ramses Barden sidelined Sunday.
"Whoever us ready to play is going to play and we showed ourselves well today," Cruz said.
Before their collapse, the Browns looked sharp as the Giants made the gaffes that led to points.
Bradshaw fumbled when the ball hit guard Chris Snee's shoulder gave the Browns a quick break at the New York 22 and Richardson took care of the yardage with runs of 7 and 15.
Wideout Gordon then beat double coverage, although with no cornerback in sight, for a 62-yard score and a 14-0 edge that didn't last long.
NOTES: Cleveland lost MLB D'Qwell Jackson, one of its defensive leaders, to a concussion. CB Dimitri Patterson hurt an ankle and DT Ahtyba Rubin to a lower leg injury. Giants backup RB Andre Brown left with a head injury and DE Osi Umenyiora left immediately after the game to be with his son, who was hospitalized by an asthma attack. ... Richardson finished with 81 yards rushing and 47 receiving. ... Weeden went 22 of 35 for 291 yards, while Manning was 25 of 37 for 259. Manning has won eight straight against AFC teams ... Coughlin trails only Steve Owen, who coached the Giants to 153 wins in 23 seasons. This is Coughlin's ninth with New York.
Online: http://pro32.ap.org/poll and http://twitter.com/AP_NFL