Granit Xhaka’s goal in the first half at the Emirates Stadium put Arsenal, leaders in the Premier League, ahead of Sporting.
Goncalves, a Portugal midfielder, beat Arsenal goalkeeper Aaron Ramsdale with a stunning strike from 46 yards out, forcing extra time.
Goncalves’ sudden strike was like David Beckham’s amazing long-range shot for Manchester United against Wimbledon in 1996, which made him a superstar.
With the score at 1-1 on the night and 3-3 overall, penalties were needed to break the tie.
After Nuno Santos scored the winning goal and Antonio Adan saved Gabriel Martinelli’s attempt, Sporting won unexpectedly.
In an effort to protect his key players, Arsenal manager Mikel Arteta made five substitutions in the first half, which led to the injuries of defenders William Saliba and Takehiro Tomiyasu.
Since winning the Cup-Winners’ Cup in 1994, Arsenal has not won a European trophy, and their wait will continue for another year.
In any case, the Heavy weapons specialists would happily trade Europa Association accomplishment for a hotly anticipated Chief Association title.
In the Premier League, Arsenal is five points ahead of Manchester City, who is in second place, as they try to win their first title since 2004.
Sporting’s win over Middlesbrough in the UEFA Cup in 2005 was their first in England.
After fielding a strong team in the first leg in Lisbon, Arteta rested Bukayo Saka, Martin Odegaard, Leandro Trossard, Ben White, and Thomas Party for Sunday’s Premier League matchup with Crystal Palace.