Goalkeeper Yann Sommer ensured Basle returned to Switzerland with a slight advantage after a hard-fought 0-0 draw in Israel.
Sommer denied Maccabi Tel-Aviv striker Eran Zahavi 18 minutes from time as a tight contest ended goalless.
The home side started and finished strongly, but were unable to make their periods of pressure count to leave the tie in the balance ahead of next week's second leg.
Maccabi began in positive mood and midfielder Maharan Radi and striker Barach Yitzhaki both had shots at goal inside the opening six minutes with the latter forcing a save from Sommer.
However, the Swiss side, who started their European campaign in the Champions League in the same group as Chelsea and Schalke, rallied and after Philipp Degen had headed wide, fellow defender Gaston Sauro tested goalkeeper Juan Pablo Colinas with a 20th-minute effort.
But as the break approached, it was Maccabi frontman Zahavi who came closest to breaking the deadlock with a 38th-minute shot which flew wide.
Basle returned in determined fashion and Serey Die saw a 55th-minute effort blocked seconds before fellow midfielder Taulant Xhaka fired wide.
But Maccabi's Omri Ben Haroush called upon Sommer with 28 minutes remaining, and the goalkeeper was in action once again 10 minutes later to keep out Zahavi's attempt.
Radi had an 83rd-minute shot blocked with the home team desperate to take a lead into next week's second leg, but Colinas had to keep out substitute Valentin Stocker's effort at the death to secure a draw.