LOS ANGELES – Between an interception that ended one drive and a fumble that set up the Los Angeles Rams to take a 14-point lead in the fourth quarter, seven consecutive 49ers drives ended with punts.

So there was little reason to believe this would be the day the 49ers snapped their franchise-worst 13-game losing streak.

But on the 49ers’ sideline, there was some hope being shared by one of the most respected players remaining on a decimated roster.

Veteran Zane Beadles, making his first career start at center, gathered the team’s makeshift group of offensive line to offer some encouraging words. He told them to forget everything that had already occurred this day at the Los Angeles Memorial Coliseum.

“Let’s get this win,” he told them.

Crazy talk? It would have seemed.

But something crazy definitely happened over the final five minutes, as the 49ers inexplicably rallied for a rousing 22-21 victory over the Los Angeles Rams on Christmas Eve.

“It felt amazing,” said quarterback Colin Kaepernick, who led the incredible late-fourth-quarter charge. “It’s a feeling this team has been looking for, for a long time now. To be able to come out and get this win, it was huge for us. It’s something this team can build on.”

The 49ers (2-13) had not experienced the sensation of winning since defeating the Rams, 28-0, at Levi’s Stadium in Week 1. It appeared as if the 49ers would enter the final week of the season with the No. 1 overall draft pick in their grasp with another loss in the finale to the Seattle Seahawks.

Instead, Kaepernick came up with some late-game heroics. He ran for a 13-yard touchdown. Then, he hit wide receiver Rod Streater on a 10-yard scoring pass with :31 remaining. The 49ers trailed 21-20 when coach Chip Kelly decided to go for two points and the win.

“I had a feeling we were going to go for two,” Kaepernick said. “And I was excited when he said we were going for it. I think the whole offense was (excited) and the whole team was. The play he called was a play I think everybody on our offense knew was going to get called. We had great confidence in. And it worked out great for us.”

Said 49ers cornerback Rashard Robinson, “I think the whole team wanted that. What else did we have to lose?”

Kaepernick was given a run-pass option. He faked a handoff to running back Shaun Draughn, then rolled right and took what the Rams defense was giving him.

Streater was the first option in the end zone. Kaepernick had two other pass targets in the progression if the Rams’ defense came up to jam his running lanes. But the Rams afforded Kaepernick enough of an opening to allow him to leap over defensive tackle Michael Brockers and get into the end zone for the go-ahead points.

Robinson preserved the victory with his interception of a Jared Goff pass at the San Francisco 42-yard line with :16 remaining.

“Kap made an exceptional play,” 49ers veteran safety Antoine Bethea said. “And when the defense got back on the field, Rashard, he made a great play. It was definitely a team effort.

“It just feels good. It’s a long time coming. It’s been a long time since we felt this way. The way we won it, it speaks volumes on our team, our character, the pride we play with. I’m just happy for the guys.”

Kelly said it was no surprise to him that the 49ers battled hard to break the losing streak. After Kaepernick’s two-point conversion and, again, after Robinson’s interception, the 49ers’ sideline erupted in spontaneous joy and jubilation it had not experienced in 3 ½ months.

“I’m around them every day,” Kelly said. “And I’ve said all along what I think about these guys, in terms of their approach. I think it’s been great. What you saw today is what we see every day. There’s an energy and a spirit to them.”

Bethea said the team has stuck together and not splintered during one of the worst times in franchise history.

“We talk about family,” Bethea said. “That’s what family is. Regardless of the good times, the bad times, the ugly times, you got to stick together. We started this journey together, we got to end it together. No finger pointing. Come to work every day and try to get better. It feels good.”

A week ago, Kaepernick talked about the 49ers lacking a winning culture after the club’s 41-13 loss to the Atlanta Falcons. The string of three consecutive trips to the NFC Championship game seemed like such a long time ago.

The 49ers have arrived at this point after Jim Harbaugh’s final team went 8-8, followed by Jim Tomsula, who went 5-11 in his only season. Things have only gotten worse in Kelly’s first year.

Kaepernick expressed encouragement about what the future could hold.

“This is a step toward building that culture,” Kaepernick said. “And I think realizing the huge plays we had in this game that allowed us to win. Whether it’s (Tramaine) Brock’s interception, Rashard’s interception, those are huge plays that we can build on, (and) also, to have two scoring drives at the end of the fourth quarter to win a game. Those are things we have to understand we have to do on a weekly basis in order to win.”

Kaepernick’s future with the 49ers might be murky. He is expected to opt out of his contract before the start of the new league year in March. It is uncertain whether the 49ers will make a push to re-sign him as a free agent.

But many of the young players feel like the game Saturday provided an example that will follow them throughout their careers.

“How we played in that second half, that was something major,” Robinson said. “That’s going to stick with me. I’m never going to forget this game.”