Blues enjoy Euro cruise

Martina and Baines also provided balls from the flanks.

Martina put one on Rooney’s head again in the 25th minute but he could not direct it goalwards.

And it was a defender who got the opener as summer signing Keane scored his first for the club on the half-hour.

Baines swung in a cross after a corner was poorly cleared and former Manchester United and Burnley defender Keane rose to head home at the back post.

Trouble flared at the away end after the goal, which caused the match to be halted briefly as police and stewards moved in.

Some visiting fans spilled out of the stand and objects, including chairs, were thrown at the home fans in the corner of the Park End before order was restored.

It got worse for the visitors as Everton doubled their lead thanks to a fine assist from Rooney, Gueye slotting into the bottom corner just before the break.

Another Martina cross in the second half was nodded wide by Rooney as the Toffees looked for the third goal that would all but end this tie even before the second leg next week in Croatia.

But they needed keeper Jordan Pickford to be alert to deny Franck Ohandza with a fine save or Hajduk could have headed home with a vital away goal.

EVERTON (4-2-3-1): Pickford; Martina, Williams, Keane, Baines; Schneiderlin (Davies 45), Gueye; Mirallas (Besic 76), Klaassen (Calvert-Lewin 62), Lookman; Rooney. Subs: Stekelenburg, Jagielka, Lennon, Holgate.

Hajduk (4-3-3): Stipica; Juranovic, Nizic, Carbonieri, Memolla; Gentsoglou (Basic 85), Radosevic, Barry; Vlasic, Ohandza (Said 66), Kozulj (Erceg 66). Subs: Letica, Bosancic, Sehic, Tudor.

Referee: Ivan Kruzliak (Slovakia).