The former Arsenal and Real Madrid winger pounced on an error by Betis goalkeeper Adrian and smashed the ball into the top corner after 12 seconds at the Sanchez Pizjuan before Federico Fazio made it 2-0 with a fifth-minute header.
Reyes, given a rousing ovation when he was substituted in the second half, made the most of more woeful Betis defending to make it 3-0 in the 33rd minute and then crossed for Fazio to score the fourth two minutes before half-time.
Betis's Ruben Perez picked up two yellow cards in five minutes midway through the second period before they pulled a goal back through Ruben Castro with just over 20 minutes left but Ivan Rakitic hit Sevilla's fifth in added time.
Betis are sixth on 19 points with Sevilla a point behind in seventh.
Sevilla had 45 per cent of possession during the victory, with 22 shots, including 13 on target.
Álvaro Negredo, who went off due to injury in the 84th minute and was replaced by Babá, made four attempts on goal – the most of any Sevilla player.
Los Verdiblancos attempted just five shots, with only three on target, generating their opportunities while having possession for 55 per cent of the contest.
Rubén Castro had three shots for Betis, more than any of his team-mates.