Basel were on their way to an important away win after goals from Albian Ajeti and Alderete Fernandez.
PSV's new Portuguese winger Bruma had given the Dutch giants a 14th minute lead but with a minute of normal time remaining it looked to be Basel's night.
Madrid plans 'robust' security for UCL final
But then late substitute Sam Lammers put them back in business with an 89th minute equaliser before Malen grabbed an unlikely decider in the second minute of injury time.
In other ties Tuesday Dinamo Zagreb put one foot in the next round with a 2-0 win at Georgians Saburtalo and Copenhagen beat Welsh outfit The New Saints by the same margin.
Olympiakos and Viktoria Plzen ended goalless while APOEL go into their second leg against Sutjeska Niksic with a 1-0 away win.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ