Porter and Christian Wood returned from one-game suspensions for conduct detrimental to the team. Wood added 22 points and 11 rebounds to help the Rockets snap an eight-game losing streak.
Jalen Green also scored 22 points and Eric Gordon had 19 for Houston.
"We just needed this one, man," said Porter, who had nine points and eight assists. "We had a couple that we could've got. ... We wanted to start the year off the right way."
Bradley Beal led Washington with 27 points. He fouled out with 9:10 to play on his second offensive foul. It was the three-time All Star's first disqualification since Nov. 29, 2017, and the first of his career before the final two minutes of regulation.
Kentavious Caldwell-Pope added 26 points, and Kyle Kuzma had 24 for the Wizards. They failed in their bid for their second pair of consecutive wins since the start of December.
"Our overall approach was, I thought, a little lackadaisical," said Wizards coach Wes Unseld Jr. "You're fighting human nature? I don't know. But we can not look at anyone's record or how many games they've lost in a row - whatever that may be. We're in no position to do that."
The Rockets started the fourth on a 7-0 spurt to push their lead to 10, and were still up seven when Beal fouled out. The rest of the Wizards responded, first tying it at 102 on Raul Neto's contested layup.
They then battled from five down inside the final minute, when Caldwell-Pope's 3-pointer closed it to two before Neto's drive resulted in a tying goaltending call.
Porter had the decisive say on the next possession when he sank a 24-footer over Neto's outstretched arm.
"We ran a wiper play and it was either for me or Jalen," Porter said. "Whoever Neto was guarding, that's who we favored to get the last shot. They switched. Once they switched, I knew I had to be aggressive and take that last shot.
A video review restored 0.4 seconds to the clock, and Kuzma's catch-and-shoot attempt was off target after Washington's timeout.
Rockets: Opened the game on a 12-2 run. ... G Garrison Matthews drew a charge from Kuzma with 2:13 left in the first quarter, Corey Kispert with 11 to play in the second, and Beal with 4:50 left in the half.
Wizards: Neto played for the first time since Dec. 23 in his return from health and safety protocols. ... Unseld said C Thomas Bryant (left knee) is getting closer to his return. "He should be available the next week or two, that would be ideal," he said. ... G Spencer Dinwiddie, G Aaron Holiday and F Rui Hachimura have cleared health and safety protocols, but remained out as they regain their conditioning.
Silas disputed the idea that Saturday's incidents in a home game against Denver, resulting in suspensions for Wood and Porter, were indicative of poor team culture.
"Nobody ever said anything about our culture until two games ago," Silas said. "And I think sometimes people overreact when stuff happens."
Rockets: Host Dallas on Friday night.
Wizards: At Chicago on Friday night.
Rockets slip by Wizards to break 8-game losing streak
Houston Rockets vs. Washington Wizards: Full Highlights