The defending champions are now three points clear of Real Madrid, who have played two games fewer and face Deportivo la Coruna later on Wednesday.
Messi’s 501st Barca goal opened the scoring, before Andre Gomes smashed in.
Roberto Torres gave the away side hope, but further strikes by Gomes and Messi, two from Paco Alcacer and Javier Mascherano’s first Barca goal followed.
After Messi’s 12th-minute opener, fans held up their shirts as they mirrored the Argentine’s celebration of a 93rd-minute winner – his 500th goal for Barca – at Madrid on Sunday.
That 3-2 victory re-opened the title race in dramatic fashion, but Barca must hope Madrid slip up in one of their six remaining matches if they are to defend last season’s success.
Osasuna’s defeat means they will be relegated if Leganes beat Las Palmas later on Wednesday.
After Torres curled past Marc-Andre Ter Stegen just after half-time, they were buried by four goals within 20 minutes.
Messi’s second of the night was the pick of the bunch as he skipped past a series of challenges and fired home, shortly after Gomes had put Barca 3-1 up with his second, tapping in after Gerard Pique’s header struck the post.
Argentina forward Messi has now scored 49 goals this season in all competitions, from 48 games.
Mascherano’s first goal in 319 games for Barca was thumped home from the penalty spot after Messi had been withdrawn.
It was the 32-year-old’s third goal in senior club football, having scored twice during three years at previous club Liverpool.
