Guimaraes conceded in just the third minute but a first-half penalty from Andre Andre dragged the hosts level at the break, while Jonathan Alvez would be the match-winner for Rui Vitoria's surprise title challengers, striking in the 82nd minute after coming off the bench.
Moreirense then had a goal ruled out for offside soon after and Guimaraes held on for victory, edging ahead of Benfica at the top of the standings.
Guimaraes moved to 26 points with their fifth consecutive victory in the league, one ahead of the reigning champions, who face Academica on Sunday.
It has been a stunning season so far for Guimaraes, who have never won the Primeira Liga, and finished 10th in 2013-14.
Moreirense stunned their hosts early at the Estadio Dom Afonso Henriques with Elizio heading into the net after just two minutes but when Bernard Mensah went down in the box in the 33rd minute, Andre Andre made no mistake from the spot to make it 1-1.
In a relatively dull second half, Alvez made the difference nine minutes after coming off the bench, with the Uruguayan scoring his fourth goal of the season.
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