KANSAS CITY, Mo. -- It took Damien Williams some time to get there, but he's finally finishing the season where he started it, as the featured back for the Kansas City Chiefs.

Williams scored three touchdowns in Sunday's divisional round playoff win over the Houston Texans, the first on a 17-yard pass from Patrick Mahomes and the others on short runs. He also played 62 of the 64 offensive snaps, compared to one each for the Chiefs' other backs, LeSean McCoy and Darwin Thompson.

That seems to firmly establish Williams as the back the Chiefs hoped he would be when the season started, their full-time replacement for Kareem Hunt. Hunt rushed for 2,151 yards and 25 total touchdowns during nearly two seasons in Kansas City, but the Chiefs released him late last season after video surfaced of him kicking a woman outside of his residence.

Williams also played well for the Chiefs late last season and in the playoffs. But mainly due to injuries to Williams, the Chiefs at one time or another were forced to turn to McCoy, Darrel Williams, Spencer Ware and Thompson for help in their backfield this season.

That's been a change for the Chiefs, who in recent seasons had dominant backs like Hunt and Jamaal Charles.

"Each situation is different," offensive coordinator Eric Bieniemy said. "In the past we've been blessed and fortunate to have a guy that can just assume the role. Now we're in that situation we feel that six legs are better than two. We just want to make sure we're maximizing the opportunities that we have with these players that all bring something different to the table.

"Whatever running backs are available, we expect those guys to play big. That's what we're counting on."

Of late, that's been Damien Williams. He took a wide majority of the playing time in the final two regular-season games as well as the win over the Texans.

"We've got three good backs that we can move in and out and we feel comfortable with," coach Andy Reid said. "Between the three of them, they all give you a different flavor. We're good with all of them."

With Darrel Williams and Ware on the injured reserve list, the Chiefs appear to have selected Damien Williams over McCoy and Thompson. Williams wound up leading the Chiefs in the regular season in rushing with 498 yards and seven total touchdowns but took no credit for that.

"It's all on the line," Williams said. "[Tackle Mitchell Schwartz] tried to give me the credit, but I'm going to give them the credit. I'm feeling confident behind those guys and they're feeling confident, so we're going to keep this thing rolling."

Williams missed most of training camp because of a sore hamstring. He was back for the first two games of the regular season, then missed two because of a knee injury. He also sat out three games later in the season because of sore ribs.

Williams said he feels stronger at this point of the season than he otherwise would because he had so much inactivity earlier.

"I feel great and I'm running like it," he said. "Being as fresh as I am, you hit the hole a little [differently]."

His three touchdowns against the Texans give him seven in the playoffs in his two seasons with the Chiefs, including two postseason games last year. That's a Chiefs playoff record. He has two more playoff touchdowns than Travis Kelce, who also scored three times against Houston.

"He looked fresh and healthy," Reid said of Williams. "We'll just keep building on that."