Henrik Larsson squandered a late penalty kick as Celtic's bid to reach their first European final for 33 years remains in the balance.
Boavista goalkeeper Ricardo, after Eder had handled an Alan Thompson shot, superbly saved Larsson’s 76th-minute kick.
The Swedish striker had earlier struck the equaliser for Celtic who had fallen behind early in the second half to an own goal from Joos Valgaeren.
Boavista defended in depth but also looked dangerous on the break in a keenly fought contest that saw four of their players booked in a torrid 15-minute spell in the second half.
The Portuguese were much the happier with the draw but Celtic have already proved in the UEFA Cup that they can produce unlikely results away from Glasgow.
Celtic stamped their authority on the game from the start and John Hartson fed Larsson with an intelligent through ball but the angle was too tight and the chance was lost.
The Scottish champions had two strong penalty claims turned down in the first quarter of an hour when the ball struck the hands of Filipe Anunciacao and then Fernando Avalos, but the Belgian referee Frank De Bleeckere was unimpressed.
For all their possession, Celtic did not trouble Ricardo in the Boavista goal in the first half and too often the final cross into the area was poor.
The Portuguese side had a couple of chances themselves with Brazilian striker Duda shooting against Bobo Balde from good position and Luiz Claudio trying his luck from distance.
Celtic Park was stunned three minutes after the break when Boavista snatched the lead when Anunciacao crossed and Valgaeren touched the ball past his own goalkeeper.
Celtic's response was immediate with Petrov cushioning a Neil Lennon cross into the path of Larsson who drilled the ball past Ricardo.
The game opened up after that and Robert Douglas produced fine diving save to keep out a 20-yard free-kick from Luis Pedrosa after Lennon had given away a free-kick.
Hartson should have scored after 73 minutes but Ricardo brilliantly saved his low shot from six yards.
Then came Larsson's penalty miss and Hartson was unfortunate not to give Celtic a victory when his 85th-minute shot was blocked on the line by Paulo Turra.
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