The goals were scored at the 22- and 26-minute marks as the Oilers (9-4 overall, 3-0 in league) outshot the Spartans (8-5-1, 2-1), 7-4, in the first half.
"We didn't play our best game," said Schurr coach Tomas Haynes. "Defensively, we'll play better next game. Some of our better players didn't have their game today."
Haynes added the team was expecting a foul to be called by the referee - which wasn't - when the second goal was scored and caught the Spartans off-guard.
"We weren't anticipating where the ball was going to be," he said. "The midfield is usually our strength and kind of hurt us today. When any team scores a goal it's a little down for you. We were looking for a foul and didn't get it and the team has still got to play through."
The Spartans tried to rally late in the second half as Miguel Mendoza launched a hard shot nearly 30 yards out to the left of the diving Oiler goalkeeper and into the net at the 78-minute mark.
A minute later, Schurr just missed tying it up as a loose ball in front of an almost open net was booted away by the Oiler goalkeeper.
Schurr outshot Montebello, 11-6, in the second half and takes on San Gabriel High at home on Thursday.