CINCINNATI — After the Giants lost their starting quarterback, they held off a late rally by the Joe Burrow-less Cincinnati Bengals.

Daniel Jones went out with a hamstring injury in the second half of the Giants’ 19-17 win on Sunday. The team’s third straight victory moved the Giants (4-7) into a first-place tie with the Washington Football Team in the woeful N.F.C. East, and comes after they lost the first five under first-year head coach Joe Judge.

It remains to be seen when or if Jones will back for next Sunday’s meeting with the Seattle Seahawks. He is scheduled to have a magnetic resonance imaging test on Monday.

“I won’t say I’m optimistic at this point right now,” Judge said after the game. “No, I don’t want to go ahead and say yea or nay because I don’t have the medical information. You know, I’m sure he’s going to try everything he can.”

Jones went down after completing a short pass in the third quarter with the game tied, 10-10. He returned for two plays on the next series but then was relieved by backup Colt McCoy.

“I’m certainly not discouraged,” Jones said. “You know, I think it’s tough to tell exactly what it is right now.”

Running back Wayne Gallman ran for a two-yard touchdown in the first quarter, giving him a touchdown in five consecutive games, the longest such streak for the Giants since Saquon Barkley scored in five straight games in 2018. Gallman, who secured the starting job after Barkley and Devonta Freeman went out with injuries, scored three total touchdowns in his first three seasons. He finished with 24 carries for 94 yards against Cincinnati.

Brandon Allen, who was promoted from the practice squad, started at quarterback for the Bengals (2-8-1) in place of the dynamic Burrow, who suffered a season-ending knee injury in last week’s loss to Washington.

Allen couldn’t keep the Bengals moving. He was 17-for-29 for 136 yards, and Cincinnati mustered just 155 total yards of offense. It wasn’t all his fault: Passes were dropped, and with Joe Mixon on injured reserve, the Giants didn’t have to worry about a Cincinnati running game. The Bengals went three-and-out four times and killed drives by fumbling twice.

Nonetheless, the Bengals had a chance late. A one-yard touchdown pass from Allen to Tee Higgins — set up by a pass-interference penalty in the end zone — got the team within two points with 2:33 remaining.

Cincinnati got the ball back, but Allen fumbled while being sacked with 57 seconds left to seal it for the Giants.

“We never got our rhythm, our first-down efficiency is really where it got us,” Cincinnati Coach Zac Taylor said. “We were in a lot of second-and-8s, second-and-9s, second-and-10 it felt like, and that’s not a great recipe against that defense.”

One of the few Bengals highlights came in the first quarter after Gallman scored, set up by a 53-yard pass from Jones to Evan Engram. On the ensuing kickoff, Brandon Wilson took the ball from three yards deep in the end zone, found a seam in the middle and rumbled for a 103-yard touchdown, the longest in franchise history.

Before he departed with the injury, Jones was 16-for-27 for 213 yards. Engram caught six passes for 129 yards.

“I don’t think you can compare this year to any other year,” Judge said. “However, I am proud of our players, of the way our players are working. I’m proud of the improvement they’ve made. I’m proud of how they come to work every day.”