Inter ran riot in the first half, with Hakan Calhanoglu netting direct from a corner to open the scoring.
Edin Dzeko finished off a fine move for 2-0 before Denzel Dumfries headed in.
Simone Inzaghi’s team are a point behind city rivals and league-leaders AC Milan, who beat Salernitana 2-0 on Saturday.
Roma are fifth after a seventh loss in 15 games left them on 25 points. They are nine behind fourth-placed Atalanta, who won 3-2 at Napoli.
Saturday’s result equals the biggest home defeat Mourinho has suffered as a manager – along with Manchester United’s 3-0 Premier League loss against Tottenham at Old Trafford on 27 August 2018.