"Our best chance is to have him," Jones said Thursday.
Johnson is 1-1 since Tony Romo broke the pinkie on his throwing hand. He threw three interceptions in the loss and passed for only 122 yards in the win, prompting speculation that third-stringer Brooks Bollinger may go in at the first sign that Johnson is struggling.
"No, I don't see that," Jones said. "That would not be fair to our ability to win the game. We have got a guy who has years and years of making decisions here. We have every reason to believe he can make decisions and make the throws to win this game for us."
Johnson's experience is a big plus, but the Cowboys (5-3) may need Bollinger's better mobility and stronger arm against the division-leading Giants (6-1). However, Bollinger has only been around since Week 2 and has hardly thrown to the first-team receivers.
Jones said he's confident coach Wade Phillips and offensive coordinator Jason Garrett know if and when to make a change.
"Those guys have a good feel for it. I wouldn't touch it," Jones said. "They have spent hours and hours over the last couple of years with Brad. They know where Brooks is and where he is right now. I am totally and completely satisfied with their timing on any decision they make regarding the quarterback."
Jones spoke after a news conference announcing that the Cowboys and Dallas Mavericks will co-host the 2010 NBA All-Star game at the football team's new stadium.
The Cowboys are a heavy underdog Sunday, partly because of all their injuries. Romo is among several key starters who will be missing on offense and defense. Tight end Jason Witten, the NFC's leading receiver, could be among the absences because of a broken rib.
After playing New York, Dallas will have a bye. The injured players are all expected back Nov. 16 at Washington.
Jones dismissed the notion his team is trying to get through this game and reload against the Redskins.
"Just the opposite," he said. "This is a pivotal game. Every aspect of this game takes on the same priority as if this was a playoff game. ... In this case, the upside has so much more bearing our future than the downside that you got welcome a game like this."
Besides, players have revenge on their mind. New York beat Dallas in the playoffs last season.
"You don't have to conjure up any reasons to dislike these guys," Jones said. "They took something away from us last year that was very important to us. That is all we need. ...
"I am very confident. I know how the players are approaching the game. Everybody has got their head in the right place. This is a great opportunity for us to go to New York to play the world champs. This could really do something for our team to have success."