Michel Bastos' brace earned Lyon a second successive Champions League win which takes them clear at the Group B summit.
The Brazil wideman smashed home a sixth-minute penalty - but it is his second, a venomous 20-yard effort, which will live long in the memory.
Penalty-taking goalkeeper Vincent Enyeama pulled a goal back for Hapoel with 11 minutes remaining, but Miralem Pjanic made it 3-1 in added time.
Lyon keeper Hugo Lloris was extended by Deddi Ben Dayan's early effort from long range but the opener was not long in coming at the other end. Walid Badir fouled Jimmy Briand in the penalty area and Michel Bastos stepped up to emphatically find the corner of the net.
The next serious threat to either goal came when Aly Cissokho's cross was met at full tilt by Bafetimbi Gomis, who improvised a volley which was turned aside by Enyeama.
Kim Kallstrom's wildly ambitious bicycle kick from the edge of the box flew well over the crossbar before Hapoel pressed and Lloris stood firm to push away as Sahar's curler from 20 yards was too central.
Enyeama was unconvincing as he smothered at Gomis' feet before Lloris reacted well to save after Sahar's tame shot took a huge deflection.
The France keeper caused panic in his own defence when he punched Romain Rocchi's corner straight into the ground, but Hapoel failed to take the opportunity as Anthony Reveillere's block thwarted Ben Dayan and Lyon broke quickly. Yoann Gourcuff brilliantly picked out Gomis but Eran Zahavi made a
fantastic saving challenge as the striker prepared to shoot.
There was no stopping Michel Bastos' effort from the resulting corner, though. Gourcuff's delivery was disappointing, but Ben Dayan's weak clearance fell perfectly for the Brazilian to launch a thunderous, swerving left-footed effort into the top corner from 20 yards.
Hapoel's Itay Schechter had a goal disallowed early in the second half after rounding Lloris with a glaring handball which also earned him a yellow card.
Gomis was just too high with another unconventional flick at goal and Douglas' header at the other end was saved before lively Lyon substitute Jeremy Pied drew a fine diving save from Enyeama with a 30-yard effort.
Enyeama was handed his chance to shine at the other end soon afterwards, though, slotting home calmly from the spot after Lovren hauled down Douglas at a set-piece.
Briand's shot was blocked by Douglas after Cissokho's cross was first missed by Pjanic, before goal hero Bastos departed with a hamstring problem.
However, the French side provided a final coat of gloss as Pied's effort was blocked but Pjanic followed up to beat Enyeama, who got a hand to the shot.