Wilson Eduardo gave the hosts the lead after 25 minutes but they were pegged back by Tarantini's strike in the 72nd minute.
And despite their late efforts, Leonardo Jardim's side could not find the goal that would have seen them jump above Porto and Braga at the summit.
At the other end of the table, Belenenses got their first points of the season on the board courtesy of a 1-0 home win over Maritimo.
Joao Pedro scored the only goal after eight minutes at the Estadio do Restelo, leaving bottom side Pacos de Ferreira as the only side in the division yet to get off the mark.
Elsewhere, Gil Vicente took advantage of Maritimo's slip and climbed above them into seventh place after a 1-1 home draw with Olhanense - although it could have been better had they not let slip a late goal.
Joao Vilela put the home side in front just after the half-hour mark, but they were denied all three points right at the end as Oumar Diakhite levelled for Olhanense in the second minute of stoppage time.
