Barca assistant Alfred Schreuder put the absence of Messi, who has struggled for form this season, down to a lack of fitness as he started a league game on the bench for the first time since September 2019.
The mercurial forward was brought on at half-time with the game poised at 1-1 after Ousmane Dembele's strike was cancelled out by Barca academy product Antonio Sanabria, either side of an Antoine Griezmann penalty miss.
Messi paved the way for Griezmann's goal 194 seconds into the second half, then scored a penalty after Aissa Mandi was dismissed for handling the ball on the line and doubled his tally late on to kill off Betis after Loren Moron's strike.
Pedri then capped a much-improved display for Koemen's side with a fifth goal late on as is secured a first league win in five on Sunday (AEDT).
Barca had made its worst start to a league season after six games in the three-points-per-win era but made a bright start against Betis, with Griezmann firing wide from 12 yards and Fati curling a shot off target.
Marc-Andre ter Stegen, making his first league appearance of the season, kept out William Carvalho's header before Ansu Fati and Griezmann wasted more presentable opportunities.
However, the breakthrough came 22 minutes in, as Dembele brought the ball inside Alex Moreno and beat Claudio Bravo, who got a touch to the shot but could not keep it out.
Griezmann then hit the post and was denied by Bravo from the spot after Mandi fouled Fati, and Betis were level when Sanabria guided in Cristian Tello's cross on the brink of half-time.
Messi was brought on for Fati at the break and had an instant impact, smartly dummying Jordi Alba's cross for Griezmann to slot into an unguarded net behind him.
After a lengthy VAR (video assistant referee) check, Mandi was deemed to have blocked Dembele's shot on the line with his arm and Messi had no trouble converting his fourth penalty of the season.
Moron gave the visitors a lifeline by blasting a shot past Ter Stegen after Gerard Pique flicked the ball into his path, but that proved nothing more than a consolation thanks to Messi's powerful left-footed drive and Pedri's close-range finish.