At 38 years and 140 days old, Joaquin hit his first ever hat-trick and surpassed Real Madrid great Alfredo Di Stefano, whose record as the oldest scorer of one in La Liga had stood for 55 years.
Joaquin also became only the seventh player in the league's history to score a hat-trick in the first 20 minutes of a match, after he found the net in the second, 11th and 20th minutes at the Benito Villamarin.
"I will remember this day for the rest of my life," said Joaquin, in a celebratory video message posted on Instagram.
Betis almost surrendered their advantage but held on for the win after Inaki Williams had converted a penalty and then Yuri Berchiche added a second for Bilbao.
Joaquin, who has 51 caps for Spain, began his professional career at Betis and made return to the club in 2015, after Valencia, Malaga and Fiorentina.