Roman Hubnik headed Sparta in front in the 76th minute but four minutes later Brazilian forward Jonathan Reis equalised for PSV.
The impressive Martin Zeman then looked to have won it with an 87th-minute strike only for 20-year-old Reis to level again from the penalty spot.
Danko Lazovic's shot flew over for PSV with a minute played and after a long lull Bony Wilfried chested down Ondrej Kusnir's long throw into the path of Jan Holenda but his left-foot shot sailed harmlessly over the crossbar.
PSV were enjoying plenty of possession and Hungarian ace Balazs Dzsudzsak cut in from the left in the 27th minute and his low shot from 20 yards was watched wide by Sparta goalkeeper Jaromir Blazek.
The game was evenly matched and Sparta midfielder Zeman drew a fantastic save from Andreas Isaksson with a swerving volley from just inside the box after 28 minutes.
Another chance went begging for the hosts in the 40th minute when a Wilfried cross from the right was only cleared as far as Igor Zofcak but he sliced his shot high and wide of Isaksson's goal.
Andre Ooijer was booked for tripping the lively Zeman and Zofcak curled over the resulting free-kick as half-time approached.
The second half took time to get going and Wilfried had the first chance for the hosts after 55 minutes with a shot from the edge of the box sailing over.
The Czechs went mightily close after an hour's play when Holenda's header from Kusnir's cross hit the post.
PSV threatened midway through the second half when Dzsudzsak's free-kick from the right was met by Bulgarian full-back Stanislav Manolev and his header was just off target.
Sparta forged ahead with a quarter of an hour to go when Zeman's free-kick from the right was headed home by Hubnik from six yards to send the home crowd into raptures.
However, PSV responded almost immediately as Dzsudzsak's 80th-minute free-kick was turned in by substitute Reis from 12 yards.
Wilfried shot wide as he tried to restore Sparta's lead and Zofcak volleyed wide with five minutes remaining for Chovanec's side.
The second goal did arrive in the 87th minute and Zeman provided it, latching on to Vaclav Kadlec's pass with a left-foot shot past Isaksson.
But again they let it slip as Wilfried fouled Lazovic in the box and Reis kept his cool to place his spot-kick past Blazek.