The Vikings also received strong work from senior guard Tom Flacco (seven points, three assists), sophomore forward Maliq Sanders (nine points on three three-pointers), and freshman forward Darren Gibson (six points).
"When everybody steps up, we're a tough team to beat," Klinewski said.
Senior guard Melvin Allen scored 11 and junior forward Mike Holloway added 9 with nine rebounds and three blocks for No. 8 Schalick (15-3).
The Cougars played without senior center Rashaan Holloway, who sat on the bench while recuperating from a badly bruised left arm.
Holloway, a Massachusetts recruit, said he likely would return to action on Thursday.
"We played well for 16-20 minutes," said Schalick coach Eric Cassidy, whose team trailed by 26-24 at haltime. "But it's tough to replace 6-10 [Holloway]."
Edwards collected a steal, assist, and hoop in the first quarter and contributed another basket in the second. He made a three-pointer in the third quarter, when Eastern outscored Schalick, 15-6, to take command of the game.
Barr arrived midway through the third quarter and entered the game with 2 minutes, 8 seconds to play in the period. He finished with four points, about 11 less than his average.
"Logan played a great game," Eastern coach Joe Murphy said. "With Alex out for most of the game, we needed guys to step up. Logan played his best game of the season."
Eastern 15 11 15 20 – 61
Schalick 8 16 6 7 – 37
E: Matt Klinewski 24, Logan Edwards 9, Maliq Sanders 9, Tom Flacco 7, John Scalindro 2, Darren Gibson 6, Alex Barr 4.
S: Mike Holloway 9, Tyler Lunsford 4, Tariq Furbush 2, Melvin Allen 11, DeAndre Solomon 9, Troy Johnson 2.