Jones -- who missed all of his rookie season last year because of a shoulder injury -- played extensively in part because after another wide receiver was injured.
The former Notre Dame standout made a move to get open on a slant, caught a pass from Kellen Moore and used a burst of speed to split defenders and score.
"I caught that ball and was running for my life," Jones said.
Jones also had a tackle-breaking, 18-yard punt return early in the second quarter shortly after Greg Salas, who is also competing for a roster spot, was carted off the field with an injured left knee.
"We did some of the stupidest things I've ever seen in football," Bills coach Rex Ryan said. "It was awful. A football follies play, offside on a fourth down call on defense by a lineman."
"Things like that at this level of the game just can't happen," Simms said. "I'm the quarterback. It starts with me and it ends with me."
Copyright 2015 by The Associated Press