St Johnstone’s squad was depleted by the summer departures of Nigel Hasselbaink, Paddy Cregg, Tim Clancy and Chris Iwelumo, and weakened further by injuries to Steven Anderson, Gary McDonald and Stevie May.
And they weathered an early storm from the hosts who went close midway through the first half when Jahmir Hyka’s free-kick was beaten away by Alan Mannus.
Luzern almost opened the scoring moments later when Marco Schneuwly rattled Mannus’ crossbar from 25 yards and St Johnstone had Brian Easton to thank for blocking Remo Freuler’s effort on the goal-line.
They went into the break goalless, but within two minutes of the restart they were ahead when Luzern failed to clear a corner.
David Wotherspoon laid the ball off in the direction of MacLean who prodded the ball home from eight yards out to give the Scottish Cup winners the lead and send the 1,000 travelling fans into raptures.
But on 69 minutes Luzern equalised when Schneuwly turned in the area before firing past Mannus' right-hand post.
Schneuwly and Dario Lezcano both had opportunities to give Luzern a lead before the second leg but St Johnstone held firm.
St Johnstone manager Tommy Wright said: "I'm absolutely delighted with the result. It was a very tough match - probably tougher than I thought it would be. I thought Luzern were excellent and put us under a lot of pressure.
"But we defended really well and in the second half we were better and caused a wee bit more of a threat,
"So we are pleased to come away with a draw. We had a magnificent result away to Rosenborg last year, but a draw tonight is probably a wee bit better for us."
The second leg will be at McDiarmid Park onThursday 24 July.