Paulo Fonseca's men headed into the game having been held 2-2 by Estoril in their last encounter.
The defending champions were far from at their best in this one but Josue's spot-kick proved to be enough to secure the win, which moves them four points ahead of Braga, who face Sporting Lisbon on Sunday.
Guimaraes owed much to goalkeeper Douglas in their first half, the Brazilian shot-stopper keeping Porto at bay on countless occasions, with his save from Nicolas Otamendi's acrobatic effort a particular highlight.
Porto had eased to a 3-0 victory in the Portuguese Super Cup back in August, but they needed a stroke of fortune to take the points in this one, the deadlock finally broken six minutes into the second half, with new signing Juan Quintero making the crucial impact.
The Colombia international surged into the penalty area as Porto pushed for the opener, and his efforts were rewarded as he was brought down by midfielder Luis Rocha.
Josue duly stepped up to convert, the 23-year-old scoring his second of the season to earn a hard-fought victory and keep Porto at the top of the table.
