The win also delayed Juventus’ title celebrations as it cut the lead between the two sides to one point, although Vecchia Signora could still seal the title with one game to spare with a win on Sunday.
Egyptian attacker Salah and Stephan El Shaarawy scored two goals each whilst Edin Dzeko rounded off the victory in this thrilling encounter.
Roma suffered an early scare as Lucas Castro lashed the ball into the net from close range to open the scoring in the 15th minute for Chievo, but El Shaarawy drew Roma level in the 28th minute for his first of the night. Luciano Spalletti's men were pegged back again when Inglese, unmarked, headed home Valter Birsa's in the 37 minutes to make it 2-1 to Chievo.
Having squandered a glorious chance earlier on, Salah made amends in the 42nd minute when he received a ball from the right flank and cut inside his marker before sending a deflected effort into the net to send the sides level at half-time.
El Shaarawy, clean through after being set up by Kevin Strootman, fired in at the far post from an angle to make it 3-2 in the 58th minute and Salah returned to cap his brace after a delightful Dzeko through ball.
Dzeko sent a thunderbolt into the back net to make it 5-2 and Inglese scored a late consolation for Chievo but the match finished 5-3.
The brace took Salah’s tally to 15 in the current campaign, one goal more than last season’s tally of 14 strikes.
The 24-year-old has been directly involved in 11 goals in his last nine Serie A appearances (six goals, five assists).