Read and Schenn entered the night with one goal in their last 10 games, and Rinaldo ended a 22-game goalless streak by scoring his second of the season before being banished in the third period.
Vinny Lecavalier contributed a goal and an assist, sending the Flyers on a three-game road trip (Florida, Tampa Bay, and Pittsburgh) in a positive frame of mind.
"It was a confidence builder for everybody," Rinaldo said.
Rinaldo also had four penalties, and he will have a hearing with the NHL for his hit to Chad Ruhwedel's head with 15 minutes, 31 seconds remaining. A suspension could follow.
Buffalo scored a power-play goal during Rinaldo's five-minute penalty - a tip in by Cody Hodgson with 12:34 left that ruined Steve Mason's shutout.
Schenn reached the 20-goal mark for the first time, scoring on a right-circle wrist shot with 4:50 remaining to make it 5-1.
The Flyers outshot the Sabres, 37-19, and swept the three-game season series.
Sean Couturier's forechecking set up the first goal, a rebound by Read with 6:30 left in the first period.
Couturier caused an errant pass that Streit fired off the right post, and Read deposited the juicy rebound from the slot.
"I had an open net and the puck bounced right to me," Read said after scoring his 21st goal. "I couldn't get any luckier than that."
Read said coach Craig Berube had a simple message before the game: Take care of the puck, get pucks deep, and have a defense-first mentality.
"We have to get back to that mentality and get going in this last stretch of games," Read said. "The hardest-working team on the ice usually wins every night."
Read set up Rinaldo for his left-circle goal with 12:20 left in the second period, and Schenn made it 3-0 nearly seven minutes later with a spectacular tip - he was falling down in front - of Streit's power-play drive.
"Good things happen when you go to the net," Schenn said after ending a seven-game goalless streak. "It's definitely a monkey off my back."
Lecavalier scored his 19th on a wicked shot from the right circle late in the second period, a play that started on a pass from Mason to Jake Voracek. Mason collected an assist.
The Flyers were coming off a 5-2 loss in Boston on Saturday, a game that was 2-2 until a little over six minutes remained.
"To be honest, I thought we played pretty good hockey," Berube said before the game. "For most of that game . . . we matched them, and I thought we were fine. And we were playing physical and playing the right way. Then we got off track again" in the third period.
In the third period Saturday, the Flyers were outscored by 3-0 (including an empty-netter) and outshot by 22-8.
Berube said the mistakes were "correctable," and added, "I think we did correct it by going over some [pregame] stuff today and talking about things. It's basically about staying with the system and staying focused."
It also helped that Sunday's opponent was Buffalo, the NHL's worst team, with 51 points and an 8-28-3 road record.
BY THE NUMBERS
Number of regular-season games remaining for the Flyers.
Their standing in the Metropolitan Division.
Number of points behind the second-place Rangers, with one game in hand.