The Reds held a 2-0 lead from the first leg at Anfield and Mane's goal after 26 minutes essentially put the tie to bed, as Porto needed four goals to progress.
Porto had started brightly however, and applied the early pressure before Mane pounced on Salah's scuffed shot, with the effort confirmed by VAR.
The hosts continued to press at the Estadio do Dragao as efforts from Yacine Brahimi and Jesus Manuel Corone were blocked by Liverpool keeper Alisson before the interval.
Liverpool doubled their lead on 65 minutes when Trent Alexander-Arnold picked out Salah but Porto hit back minutes later when Eder Militao headed home a corner.
Roberto Firmino headed effort restored Liverpool's two-goal advantage on the night and Virgil van Dijk completed the scoring with another header, after Mane had flicked a corner into his path.
Liverpool will take on Catalan giants Barcelona in the last four, with Spurs and Ajax contesting the other semi-final clash.