Henrik Larsson's stoppage-time winner brought the result a markedly superior Celtic team deserved against shockingly weak visitors. Perversely the home team were almost denied victory when Alan Stubbs's first-half opener was equalised four minutes from the end by Sven Soderstrom's thundering 25-yard drive.
Celtic produced a variety of fine scoring efforts last night before Stubbs made the breakthrough. Craig Burley had hit a 30-yard drive with the outside of his right foot, dipping just over the bar, before Harald Brattbakk produced a venomous volley from Tosh McKinlay's long cross from the left which forced Espinha into an exceptional save. Larsson then rattled the crossbar with a 25-yard free-kick.
Vitoria had looked vulnerable at set pieces - Marc Rieper heading a McKinlay corner marginally high - and it was from one of these that Stubbs struck. McKinlay delivered a free-kick from the left to the forehead of the big defender and, unattended, he bulleted the ball low to the left of Espinha.
Vitoria were, by comparison, poor in forward areas. One slick move between Soderstrom and Kasongo, leaving the former with a reasonable chance, collapsed with a feeble and poorly-placed shot which Jonathan Gould saved comfortably.
The Portuguese weakness was such that they even missed a penalty midway through the second half. Stephane Mahe foolishly tripped the substitute, Edmilson, and Gilmar weakly chipped the conversion attempt over the bar.
But when Celtic next won a corner, McKinlay's accurate delivery allowed Larsson to head powerfully and accurately, only to see Quim Berto block the ball on the goal line.
Celtic: Gould; Hannah, Rieper, Stubbs, Mahe; Donnelly, Burley, Lambert, McKinlay; Brattbakk, Larsson.
Vitoria Guimaraes: Espinha; Quim Berto, Arley, Alexandre, Kasongo; Milovanovic, Costa, Soderstrom, Riva; Gilmar, Geraldo.
Referee: O Sarvan (Turkey).