Celtic could have forged ahead after just a minute when Mark Burchill was given room to roll the ball into Larsson's path, but the Swede was tame with his shot.
Hapoel took a while to find their courage and Lubomir Moravcik had more room than he enjoys in the Scottish Premier League.
The Slovakian playmaker curled one sublime shot just over the bar, in the 10th minute. Gradually, the Israelis overcame their awe of the huge crowd and could have silenced it had Istvan Pishont's shot not narrowly cleared the bar, or Kfir Udi managed to round Oliver Tebily when released by Ronen Harazi.
Celtic took heed of the warning and gave themselves a cushion in the 24th minute when Larsson opened the scoring with his seventh goal of the season. The creator was Moravcik. The Slovakian lofted a wonderful ball over the head of Gereson, the Hapoel central defender, which Larsson seized upon and showed great poise to loft the ball over the onrushing goalkeeper Elimelech.
Larsson collected his second goal of the night in the 50th minute with an emphatic penalty after Stephane Mahe's driving run into the box was rudely halted by Gereson. The Swede was forced to wait until Elimelech had completed his time-wasting antics - for which he was booked - before driving a right-foot spot kick just inside the goalkeeper's right hand post.
Stubbs then struck the top of the bar with a header before Elimelech made a wonderful save from Craig Burley's netbound header in the 68th minute. At the other end, Gould ensured Cimirotic's menace did not yield an away goal.
Celtic (4-2-2-2): Gould; McNamara, Stubbs, Tebily, Mahe; Lambert, Burley; Moravcik, Petta (Blinker, 85); Burchill, Larsson. Substitutes not used: Kharin (gk), Petrov, Mjallby, Riseth, Brattbakk, Johnson.
Hapoel Tel Aviv (4-5-1): Elimelech; I Bakhar, Gereson, Ohaion, Antebi; Rupnik, Pishont, Toema (Gohen, 72), Udi, Cimirotic; Harazi (Tikvah, 63). Substitutes not used: Hillel (gk), Racunica, Balali, Afek, Rahmin.
Referee: F De Bleeckere (Belgium).