Betis held their own in a tight first half but they had no answer to Barca's onslaught after the break. Ivan Rakitic opened the scoring before braces from Messi and Suarez capped a wonderful display.
The result sends Ernesto Valverde's side 11 points clear at the top of the table, with Atletico Madrid having drawn with Girona and Valencia losing at Las Palmas on Saturday.
Betis had won their previous two matches, scoring eight goals in the process, and they stayed true to their bold pressing approach under Quique Setien during a keenly contested opening 45 minutes.
Barca's control had been growing, though, despite the loss of Thomas Vermaelen to injury towards the end of the first half, and they deserved the lead given to them by former Sevilla captain Rakitic in the 59th minute.
Messi then fired home with aplomb after good play from Sergio Busquets and Suarez finished well from Rakitic's cross to complete a devastating spell for the visitors and leave the home fans stunned.
A mazy Messi run and finish made it 4-0 with 11 minutes left and Suarez steered his strike partner's pass high into the net in the 90th minute for a fifth, giving Barca a firmer grip on the title race and a 14th game without defeat against Betis.
The home side began on the front foot, with Andres Guardado firing narrowly wide after only three minutes, as Barca struggled to get to grips with the home side's ferocious work-rate.
The visitors slowly settled as Betis began to drop deeper, though, and Sergi Roberto missed a good chance to break the deadlock 25 minutes in when he fired Suarez's lay-off over the bar.
Messi was becoming increasingly involved and he was next to come close to the opening goal, rippling the side-netting from six yards out after Suarez had played him in with a fine pass.
The half ended in disappointment for Barca, though, as Vermaelen limped off with what looked like a hamstring problem, with Samuel Umtiti on to replace him for his first appearance in LaLiga since December 2.
The injury did little to throw the visitors out of their stride as their pressure grew in the second half and they at last found the breakthrough just before the hour mark.
Suarez's superb throughball picked out the run from Rakitic, who had plenty of time to stride towards goal and slot the ball left-footed beneath Antonio Adan and into the net.
Five minutes later, the game was effectively over. Busquets robbed Fabian Ruiz in his own half and played the ball through to Messi, who turned to face Adan and rifled a low shot into the right-hand corner.
Suarez made certain of the points in the 69th minute, the Uruguay star volleying Rakitic's cross off the turf and into the bottom-right corner after some more fine play from Messi.
Betis' fight had all but evaporated and they allowed Messi to score his 19th league goal of the season in style, the 30-year-old weaving his way into the penalty area before side-footing past a disconsolate Adan.
There was just enough time for Messi to lay on a fifth for Suarez and cap a brilliant display, the former Liverpool man blasting the ball high into the net from 12 yards out for his 100th goal in Spain's top flight after his strike partner had squeezed the ball into his path.
