A pair of goals from Marcel Sabitzer, aided by errors from Hugo Lloris, gave Leipzig control of the second leg of the last-16 tie at the Red Bull Arena.
Emil Forsberg rounded things off with a late goal to make it a 4-0 aggregate triumph for Leipzig as Tottenham's streak of games without a victory in all competitions was extended to six games.
That is the longest winless run in Mourinho's career, which has spanned 935 matches.
It is a sequence encompassing the first leg against Leipzig, which ended in a 1-0 reverse, as well as Premier League losses to Chelsea and Wolves, an FA Cup penalty shoot-out loss to Norwich City and a 1-1 draw at Burnley.
Spurs will seek to end that streak when they welcome Mourinho's old club, Manchester United, to north London on Sunday.