PSV, runaway unbeaten leaders of the Dutch Eredivisie, were left to rue a plethora of first-half missed chances and now have it all to do in the second leg in Germany.
And it was a cagey opening in an intimidating atmosphere in Eindhoven, the home fans letting off a volley of fireworks at kick-off. When the smoke cleared, the hosts had the better of the opening exchanges, Mexico international winger Hirving Lozano causing the Dortmund defence headaches down the left.
PSV midfielder Malik Tillman squandered two gilt-edged chances in front of goal. And the visitors punished PSV's profligacy, taking the lead against the run of play in the 24th minute when Malen squeezed a deflected shot into the top corner.
Tillman redeemed his earlier errors by winning a penalty in the 56th minute, which De Jong slotted calmly past Alexander Meyer.