Berry improved to 3-0 after defeating Quebec's Felix Asselin 9-6 on Sunday, while Klymchuk is also perfect through three matches with an 11-7 win over Yukon's Mitch Young.
"I think we're in a pretty good position," said Barry, who's playing in his fourth Canadian juniors. "Our game's not necessarily where we want it, exactly. I've been struggling a little bit, and thank goodness my team has kind of been holding me up. Hopefully we can take it from there and get a little better as the week goes on."
The losses dropped Asselin to a 1-1 record, while Yukon fell to 1-2.
In other Draw 4 play, Nova Scotia (2-1) cruised past Newfoundland and Labrador (1-2) 11-5, Manitoba (2-1) beat Northern Ontario (1-2) 10-4 and Alberta (2-1) slammed Nunavat (0-4) 22-2.
In women's play, B.C. skip Corryn Brown edged Carolyn Suley of Newfoundland and Labrador 7-5 to improve to 3-1 atop Pool A.
Yukon's Sarah Koltun (2-1) meanwhile scored a point in the 10th end to down Jessica Daigle (1-2) 6-5, Northern Ontario (1-2) romped past Northwest Territories (1-3) 13-2, P.E.I. (1-1) edged Quebec (1-2) 6-5 and Saskatchewan (1-2) won easily, 21-1 over Nunavat (0-4).
Manitoba's Shannon Birchard and Ontario's Jamie Sinclair each remain undefeated at 3-0.