Lukas Sedlak scored into an empty net with six seconds remaining in the third period after coming out of the penalty box.
Jones had an assist, and defense partner Zach Werenski had two assists.
Kevin Hayes scored, and Henrik Lundqvist made 40 saves, 16 in the third period, for the Rangers.
"He was phenomenal tonight as always," Jones said of Lundqvist. "We had a lot of chances in and around the paint, around the hash marks and he stoned us cold. That's what he does against us every year. [Bobrovsky] does that every night for us too, makes big saves and keeps us in games."
Hayes scored at 14:35 of the first period for a 1-0 lead eight seconds after his slashing penalty ended. Hayes got the puck after Jones turned it over in the neutral zone and scored from the right circle with a low shot past Bobrovsky's glove.
Jones tied the game 1-1 at 19:14 of the second. His first goal of the season came off a shot from the right wall that deflected off the outstretched leg of Rangers forward Mika Zibanejad.