SANTA CLARA, Calif. -- When he stepped to the podium, San Francisco 49ers head coach Kyle Shanahan's hair was still wet from the celebratory postgame shower his players gave him in the locker room on Sunday at Levi's Stadium.

It took him until his 10th game, but Shanahan finally got his first NFL coaching victory.

Rookie quarterback C.J. Beathard passed for 288 yards and two touchdowns, leading the 49ers (1-9) to a 31-21 victory over the New York Giants (1-8).

"I feel good," Shanahan said. "I feel very good. I didn't know it would take this long. It's special with the guys. I was really happy for them. These guys have been working so hard."

Beathard completed 19 of 25 passes with touchdowns of 83 yards to wide receiver Marquise Goodwin and 47 yards to tight end Garrett Celek in the second quarter. Beathard, who was intercepted once, ran for an 11-yard score in the fourth quarter.

"It feels great," Beathard said. "There's not a better feeling. That's why you play sports is that feeling in the locker room with your teammates celebrating a win."

Quarterback Eli Manning completed 28 of 37 passes for 273 yards and two touchdowns for the Giants. He started his 208th consecutive game, tying his brother, Peyton, for the second longest streak in NFL history by a quarterback, behind only Brett Favre's streak of 297.

"It's tough losing," Manning said. "You work hard every week. You go out there to execute and make plays and put your team in a situation to win, and it's not happening.

"It's disappointing. We're in this situation and we're the reason we're in it. We just have to keep working and compete every week and expect to win next week."

New York wide receiver Sterling Shepard caught 11 passes for 142 yards. Giants tight end Evan Engram caught six passes for 31 yards and a 9-yard touchdown, his fifth score of the season, tying a team rookie record. He caught a touchdown pass for the fourth straight week.

Running back Carlos Hyde rushed for 98 yards on 17 carries for the 49ers.

The last time two NFL teams with a combined one or fewer wins met this late in the season was Nov. 4, 1984, when 1-8 Cleveland beat 0-9 Buffalo 13-10.

That fact didn't tarnish the win for veteran 49ers tackle Joe Staley.

"I've been a part of a lot of wins with this franchise over the 11 years I've been here," Staley said. "This win felt just as good as winning the NFC Championship. It was unbelievable."

Beathard completed 13 of 16 passes for 198 yards and two touchdowns in the first half to help the 49ers build a 17-13 lead.

After a scoreless third quarter, Beathard extended San Francisco's lead to 24-13 on an 11-yard touchdown run with 14:53 remaining. He aggravated an injury to his right thumb, but finished the game.

Rookie running back Matt Breida increased the 49ers' lead to 31-13 on a 33-yard touchdown run with 9:19 remaining.

Manning threw a 14-yard touchdown pass to Roger Lewis Jr. with 1:02 left. Running back Orleans Darkwa converted the 2-point try, making it 31-21.

"We got schooled," Giants cornerback Dominique Rodgers-Cromartie said. "I didn't see enough relentless play, attitude, you name it. I did not see it. Everything we should have done, I felt we did not do it.

"It seems like you have two teams that came out there with their backs against the wall. You had a team that came out swinging harder than the other."

The 49ers took their first lead at home this season at 3-0 when Robbie Gould kicked a 44-yard field goal with 12:40 left in the first quarter. Aldrick Rosas answered with field goals of 47 and 42 yards, putting the Giants ahead 6-3 with 1:07 remaining in the opening quarter.

The Giants drove to San Francisco's 22 early in the second quarter, but on second-and-4, defensive end Ronald Blair III forced a Manning fumble, and strong safety Eric Reid recovered at the 15.

Three plays later, Beathard connected with Goodwin for an 83-yard touchdown, the 49ers' longest play of the season. The Giants blitzed, and Goodwin beat cornerback Janoris Jenkins' man-to-man coverage on a deep post route to put San Francisco ahead 10-6 with 7:59 left in the half.

"It was a great play call by Kyle," Beathard said. "It was the perfect play for the coverage they had. Celek and Carlos did a great job picking up the pressure. They brought an all-out blitz.

"The O-line gave me a bunch of time to get it to Marquise, the speedster, who I knew could get over the top of the coverage. He's the fastest guy in the league."

The Giants moved ahead 13-10 on Manning's 9-yard touchdown pass to Engram with 2:08 remaining in the half.

Beathard answered with a 47-yard touchdown pass to Celek. He hit Celek in stride on a crossing route, and the tight end got a block from Goodwin, then juked Jenkins on his way to the end zone, putting the 49ers ahead 17-13 with 28 seconds left.

"I saw the safety and all of a sudden Marquise came out of nowhere and just blasted him," Celek said.

NOTES: Giants LDT Damon Harrison Sr. left the game late in the fourth quarter with an ankle injury and did not return. ... Giants starting LG Justin Pugh (back) was injured in the first half and backup G D.J. Fluker (knee) in the third quarter. Neither one returned. ... 49ers LT Joe Staley (fractured orbital bone) returned to the starting lineup after missing one game. ... Giants MLB Kelvin Sheppard, who started in place of injured MLB B.J. Goodson (ankle), left the game in the third quarter with a groin injury and did not return.