Rangers took advantage of woeful defending to earn a last-16 clash with Osasuna in the Uefa Cup.
Barry Ferguson fired Rangers into an early lead
Captain Barry Ferguson gave Rangers the lead in the 24th minute when he fired home Nacho Novo's low cross.
Despite some neat play, Hapoel rarely threatened Alan McGregor's goal and Kris Boyd punished calamitous defending to score the second.
Ferguson added the third before Rangers goalkeeper McGregor was sent off and Charlie Adam scored a late fourth.
Rangers manager Walter Smith was forced to change his side after defender Karl Svensson failed a late fitness test.
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Brahim Hemdani moved back into the central defensive berth he occupied earlier in the season, with Gavin Rae slotting into midfield.
Kevin Thomson returned from injury to make his European debut for Rangers and Chris Burke was given the task of supplying ammunition for Novo and Kris Boyd.
Hapoel named the same side that defeated Rangers 2-1 in last week's first leg of the last-32 tie.
Burke appeared menacing in the opening stages and Doani was booked for fouling the winger as his mazy run took him towards the box.
Goalkeeper Shavit Elimelech then tipped an Alan Hutton header just over the crossbar after he had connected well with a Burke corner.
Rangers took the lead when Burke's pass released Novo down the right-hand side and his cut-back from the byline was rifled home by Ferguson.
Salim Toema then shot wide as the visitors tried to get back into the game.
But despite, some enterprising play in midfield, Hapoel were often toothless in attack.
Kris Boyd put Rangers two up - despite Hapoel appeals for handball
Hapoel skipper Yossi Abuksis then gifted Rangers a second goal, when his attempted crossfield pass was cut out by Boyd.
The ball appeared to hit the striker's arm, but the referee ignored Hapoel's appeals and Boyd had a simple task to score.
Rangers were comfortable in the early part of the second half and were content to let Hapoel have possession in midfield without creating clear-cut chances.
Ferguson sealed Rangers' progress to the last 16 of the competition when he converted substitute Dado Prso's cross to make it 3-0.
But there was controversy after the goal as McGregor clashed with a Hapoel player and the referee showed the Gers keeper the red card.
The game threatened to boil over as Hapoel toiled to claw their way back into the game.
Charlie Adam sealed Rangers' victory with an injury-time winner to complete a 5-2 aggregate win.
Rangers: McGregor, Hutton, Weir, Hemdani, Murray, Ferguson, Rae, Thomson, Burke (Adam 90), Boyd (Prso 64), Novo (Klos 75).
Subs Not Used: Sionko, Sebo, McMillan, Perry.
Sent Off: McGregor (74).
Booked: Rae, Novo, Murray.
Goals: Ferguson 24, Boyd 35, Ferguson 73, Adam 90.
Hapoel Tel-Aviv: Elimelech, Bondar, Doani, Antebi, Badir, Dago (De Bruno 46), Abuksis (Vermot 65), Wellington (Jolic 80), Toama, Ogbona, Barda.
Subs Not Used: Ben Shaanan, Chen, Abutbul, Peretz.
Booked: Doani, De Bruno.
Ref: Matteo Trefoloni (Italy).