The veteran 33-year-old forward opened the scoring after just three minutes and it gave him his 67th goal in the Champions League before he added a second to take his overall tally to a record 70 in all European competition.
Compatriot Jose Manuel Jurado hit the third to complete the rout.
"For him (Raul), it was a relief to get those goals, he was been under fire and it was good for him to show how strong he is in front of goal," said Schalke coach Felix Magath.
"It was good for us that we scored some nice goals and played some good football. It will give us a confidence boost, we have always played well in the Champions League, but now we need to concentrate on the league."
Schalke dominated Hapoel until the visitors grabbed a consolation goal with the last kick of the game when forward Etey Schachter scored from a simple tap in in the third minute of extra time after a mistake in the Schalke defence.
The Royal Blues may be third from bottom of the Bundesliga, but with six points from three games they are now second in Group B behind leaders Lyon, who beat Benfica 2-0 on Wednesday.
Hapoel are bottom of the table and pointless after their third defeat.
Schalke dominated their Israeli opponents at the Veltins Arena in Gelsenkirchen with Dutch striker Klaas Jan Huntelaar going close with a string of chances and he was a constant threat.
A pass from Huntelaar sent Raul through one-on-one with Tel Aviv goalkeeper Vincent Enyeama and the former Real Madrid striker made no mistake after just three minutes.
Raul doubled the hosts on 58 minutes with a simple finish after substitute Ivan Rakitic had exchanged passes with Huntelaar and the Spaniard just had to roll the ball across the line.
Spanish midfielder Jurado then secured the points for Schalke with a superbly-taken third on 68 minutes.
The Spaniard shifted the ball on to his right foot and made enough space for himself to curl a shot around the defence and in off the far post before Schechter pulled one back for the guests.
In the next round of matches, Schalke travel to Tel Aviv on November 2.