The hosts were in charge from the first whistle, but Estoril responded well to their direct approach to limit the opportunities on offer early on.
Boavista, however, did make the breakthrough midway through the first half when Yohan Tavares made an error to gift space to Uche Nwofor, who capitalised to finish emphatically from the edge of the box.
Despite looking in control, Boavista were dealt a blow when Samuel Inkoom picked up his second yellow card inside the opening 33 minutes to leave the home side with 10 men.
After being handed a lifeline by the red card, Estoril had the opportunity to get back on level terms when the referee pointed to the spot, despite a cross appearing to strike Henrique in the chest.
Leo Bonatini stepped up to take the penalty and he kept his composure to equalise just before the interval.
Boavista should have been back in front early after the break when Douglas Abner led a break before finding substitute Ze Manuel, who somehow managed to miss the target after being left unmarked in the box.
Estoril enjoyed spells on top as they looked to take advantage of the extra man, but the visitors rarely opened up the home defence in a frustrating second half.
Afonso Taira handed the advantage back late on when he picked up a second yellow card as the two sides eventually settled for sharing the points.