Celtic beat Rangers at Hampden to set up a Scottish Cup final against Aberdeen and the chance to complete a domestic treble.
Callum McGregor's superbly placed finish put the Premiership champions ahead during a dominant first half from Brendan Rodgers' side.
Scott Sinclair squeezed in a penalty after Rangers' James Tavernier had fouled Leigh Griffiths.
Goalkeeper Craig Gordon twice denied Kenny Miller in Rangers' best attacks.
But the Ibrox side could not prevent the first defeat of Pedro Caixinha's reign as manager and must now focus on securing European qualification through the league.
Celtic have already won that tournament and the League Cup and will face the Dons back at the national stadium on 27 May - the second Aberdeen-Celtic cup final this season - hoping to complete the domestic clean sweep for the first time since 2001.