The 19-year-old struck just before half-time to ensure the Lilywhites remain unbeaten at Deepdale since Simon Grayson took charge.
Earlier former Rovers man John Welsh had gone close, striking the post with a curling 25-yard free-kick after seven minutes.
The Preston captain went close again on the half-hour mark with another free-kick but Owain fon Williams did well to claw the ball wide.
At the other end, Bailey Wright hit his own post after 38 minutes and Declan Rudd denied Mamady Sidibe shortly afterwards when the Malian striker turned Michael O'Halloran's cross goalwards.
Monakana rifled in from 12 yards in first-half stoppage time however after Will Hayhurst's low cross-shot was cleared off the line.
He nearly doubled his tally after 65 minutes but his left-foot shot from the edge of the box went just over.
Substitute Lee Holmes beat everybody with a deep right-wing cross in the 78th minute but the ball bounced just wide as the hosts eased to victory.