Rooney led the line as he played the full 90 minutes, but the former Manchester United captain wasted a couple of clear openings to make a dream comeback at Goodison Park on Thursday and it was left to captain Leighton Baines to score the only goal.
In a tight match, Rooney found himself dropping deep to get involved in the play, but he regularly surrendered possession as the hosts tried to break down the stubborn Slovakian side.
Ruzomberok had plenty of chances of their own to go with their impressive defensive resistance, with Maarten Stekelenburg tipping Jan Maslo's header on to the crossbar.
Baines broke the deadlock midway through the second half, his drive deflecting in to hand Everton the advantage ahead of next week's second leg.
But it was a disjointed display from Koeman's side, who looked to be missing the dynamism provided up front by Romelu Lukaku after the powerful striker was sold to Manchester United for £75million.
Everton almost took the lead in farcical fashion after seven minutes when Ruzomberok captain Dominik Kruzliak sliced a wild clearance over his goalkeeper Matus Macik, who recovered to scramble the ball away.
Rooney rifled over the angle after 19 minutes before Dalibor Takac clipped a shot wide in a rare Ruzomberok raid forward through a congested midfield.
Persistence on the right wing from Dominic Calvert-Lewin provided another opening for Rooney, but his first touch was sloppy and the returning forward could not get a clean shot away.
A one-two with Calvert-Lewin sent Davy Klaassen through, but the debutant hit the side-netting, then a long-range Idrissa Gueye strike was straight at Macik.
Erik Daniel forced Stekelenburg into a fine save to his right after 36 minutes with a low drive before the bright Calvert-Lewin tested Macik on the stroke of half-time.
Klaassen headed Cuco Martina's cross wide as Everton built up some pressure early in the second half, with Kruzliak diverting a goal-bound Kevin Mirallas strike away from danger.
Ruzomberok continued to threaten sporadically, though, and Stekelenburg had to tip a crashing Maslo header onto the crossbar in the visitors' best chance of the match.
And that save proved crucial almost immediately as Everton finally found the breakthrough after 65 minutes.
Ruzomberok failed to clear a set-piece and skipper Baines was perfectly placed to fizz home a 20-yard drive that beat Macik with the aid of a deflection off Daniel.
Macik prevented Everton from extending their lead by tipping over a Mirallas effort, keeping his side in the contest, and Everton hold a narrow lead in the tie.