Villas-Boas, 46, obtained 21,489 votes, to just 5,224 for his 86-year-old rival, who had won his previous 15 successive elections to head The Dragons.
"What a historic night... our club is alive and today proved its strength," said Villas-Boas, in a statement issued by Porto.
Villas-Boas enjoyed his most successful managerial spell at Porto.
Aged just 33, he guided them in the 2010/11 season to the domestic double - crowned champions without losing a game - the Portuguese Cup and the Europa League.
The victory in the Europa League - beating Portuguese rivals Braga - made him at 33 years and 213 days the youngest coach ever to win a European club trophy.
Villas-Boas promised during his campaign to hire former Spanish international goalkeeper Andoni Zubizareta, who he came across while he was manager of Ligue 1 side Marseille, as sporting director.
He also pledged to install former Portuguese international defender Jorge Costa as head of the football department.
Pinto da Costa had on his part this week extended the contract of present head coach Sergio Conceicao.
Since Pinto da Costa was first elected in 1982, Porto have enjoyed unprecedented success trophy-wise - winning 23 league titles and both the European Cup in 1987 and its successor the Champions League in 2004.
However, this season things have turned sour.
The club is plagued by financial problems off the pitch and the team has struggled on it, languishing in third place in the league table 18 points adrift of leaders Sporting, who they host later on Sunday.
For Villas-Boas it will be a new challenge, having retired from coaching, to focus on the presidential campaign, when his time at Marseille ended acrimoniously in 2021.
Unlike his compatriot and former Porto coach Jose Mourinho he failed to deliver on his early promise despite high profile jobs at Chelsea and Spurs.
He lasted less than a season at Chelsea and just over one at Spurs.
Spells followed in Russia, where he guided Zenit St Petersburg to a league title (2015) and a Russian Cup success (2016), China and then the ill-fated adventure with Marseille.
