Klinewski collected 31 points with 12 rebounds, and senior guard Alex Barr scored 12 for No. 6 Eastern (9-1).
"We have to take the lessons we learned in this game into the rest of the season," said Klinewski, a Lafayette recruit. "Our effort was 110 percent. If we play this hard and execute better, we'll win a lot of games."
Howard said Paul VI is a better team after Thursday's 60-58 loss to rival Bishop Eustace.
"That loss made us stronger," Howard said. "We came back to practice the next day and realized that we have to come out and play our best every time we take the floor. We know it's not going to be easy."
Without senior point guard Ivan Robinson, who likely will be out for another two weeks with a concussion, Paul VI got strong games from Green and senior guard DeVahnte Mosley (five points, five assists).
"That's what we needed," Paul VI coach Tony Devlin said. "With Ivan out, we needed somebody else to step up."
The 6-foot-4 Green scored eight in the second quarter, when Paul VI turned up its defensive intensity, got out in transition, and outscored Eastern by 22-7.
After falling behind by 18-10, the Eagles went on a blistering, 31-5 run.
"We know we have to play every game like it's our last," Green said.
Howard, who still is hampered by an ankle injury that caused him to miss the season's first four games, grabbed eight rebounds and got to the foul line 11 times. Risse made three of the Eagles' seven three-point jumpers.
"I really liked how hard we played," Devlin said.
Klinewski played one of the strongest games of his career. He made four traditional three-point plays, ran the floor like a guard, and exhorted his teammates for 32 minutes.
"I'm hyped for every game, but I really wanted to go out with a bang in my last game against this team," Klinewski said.
Eastern 18 7 17 21 - 63
Paul VI 19 22 17 15 - 73
E: Alex Barr 12, Tom Flacco 2, Maliq Sanders 10, Matt Klinewski 31, Logan Edwards 2, Justin Fendrick 6.
P: Jay Howard 22, Matt Risse 18, DeVahnte Mosley 5, Jahvan Rosbia 7, Jair Green 18, Lonnie Moore 3.