It was 3-0 in the first half, with two goals coming from Suarez and one from Messi, as Coutinho scored a second-half penalty kick and Andres Iniesta also scored.
Unsurprisingly, Suarez and Messi were the difference in sealing an unlikely late point for Barcelona, and Sevilla must maintain great discipline and concentration over the full 90 minutes if they are to halt Barca's superstar strike duo.
Barcelona will be looking to defend their trophy they won past year and will be looking to take a step closer to completing a league and cup double in what has so far been a dominant season for the Catalans.
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She said: "I was a Macmillan nurse for a while and in that time, got to really see what the charity means to people directly or indirectly facing cancer".
Ernesto Valverde is expected to restore his big guns after resting them for the draw at Celta Vigo.
Every Barcelona player's contract sets out the bonuses they'll earn when the team wins a trophy.
And things got worse for them early in the second half.
Barca's dominance continued after the break and they found a fourth through Iniesta, who received a perfectly-weighted ball from Messi before rounding Soria and tapping home in what could be his last final appearance for the club.
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Saric responded with a huge 3-pointer and a layup on consecutive possessions to put the Sixers back up 112-102. No team have ever rebounded from a 3-0 deficit to win an National Basketball Association play-off series.
Iniesta went close for Barcelona in the 28th minute as his deflected shot hammered against the crossbar, but they did have their second goal just three minutes later.
Sevilla's replies were brief and unsuccessful, Steven Nzonzi poking wide from the best one after meeting Jesus Navas' cross. Nominally on the right but floated in midfield, setting up the first goal for Suarez and sending David Soria the wrong way from the penalty spot for the fifth.
Sevilla and Barcelona face off in the Copa del Rey final on Saturday in Madrid.
Iniesta was substituted in the 87th minute to a rousing applause from both teams' supporters amid speculation that he is playing in his final season for Barcelona ahead of a possible move to China.
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The tie was effectively put to bed in the 40th minute, Suarez exchanging passes with Messi in the number 10 pocket before finishing low past Soria.