Hapoel continued to threaten and there was a change of penalty-taker in the second half, and Shir Tzedek made no mistake, rifling his shot down the centre of the goal to make it 2-0 on the hour mark.
Tzedek went from hero to villain just seven minutes later, scoring an own goal to give Lugano a lifeline.
Hapoel edged possession on the night but theyir supporters were relieved to hear the final whistle following a stern test against the Swiss opponents.
Maccabi Tel Aviv, Israel's other Europa League entrant, saw their nine-match unbeaten run in European football halted as they were edged out 1-0 by Slavia Praha in Group A.