Laybourn said "we concentrated on penalty corners because we figured that we've got quite a good PC set up so we may as well try and get PCs and use our strength there."
City came out fast after halftime and converted early when Elle Swanson finished a penalty corner variation before Laybourn stretched the lead shortly after when she converted another penalty corner opportunity.
Country got one back towards the end of the match when a Jodie Nichol strike found the backboard after they had a period on attack.
"It's fun to play with players you don't usually play with and there is a little bit of pride involved because you're playing for something. You have a bit of banter out there," Laybourn said.
In the men's match City came from behind to clinch a 2-1 win in the final minutes of the game.
Country went one up early in the match when Liam Litchfield touched the ball in off the post.
It wasn't until early in the second half that City found the equaliser through Lloyd Gurr before securing the win four minutes from full time when Chad Cahalane found the goal.
The three match series continues on Wednesday from 6pm before the final matches on Sunday from 3pm.