The Argentine scored two free kicks to give the Catalans the lead after Ever Banega's early goal. Barca eventually raced to a 4-1 lead, but the Europa League winners clawed their way back to take it into extra time.
In the 115th minute, Messi saw a shot after another threatening free kick saved, only for Pedro – a player Barcelona confirmed wants to leave the club – popped up to win the match.
Sevilla winger Vitolo was full of praise for his side after a strong performance, but he admitted that an in-form Messi was impossible to overcome.
"Messi is the best player of all time and today he had a stormer," he told reporters. "The side put in a 10 out of 10 performance. We ran a lot – it's not easy to come back from 4-1 down against Barcelona."