Celtic effectively ended Rangers' season when Henrik Larsson's 53rd-minute goal gave his side a 1-0 win in a fraught Scottish Cup quarterfinal on Sunday.
In a match of high tension and few chances, Larsson's 28th goal of the season separated the bitter Glasgow rivals to keep alive Celtic's hopes of a league and cup double. Celtic can now look forward to a UEFA Cup fourth round first leg at home to Barcelona on Thursday.
Rangers, meanwhile, can expect to end the season without a trophy a year after completing the domestic treble.
Alex McLeish's side are also out of the League Cup after losing on penalties to Hibernian in the semifinal. They trail Celtic by 16 points in the league and were eliminated from European competition in December after finishing bottom of their Champions League group.
Rangers raised their form considerably for the Old Firm tie but could not put the finishing touches to the few chances they created.
Celtic go into Monday's semi-final draw with Dunfermline Atheltic, who won 3-0 at Partick Thistle on Saturday, and first division Inverness Caledonian Thistle after their 1-0 win at Motherwell.
Aberdeen and Livingston will replay their quarter-final tie after a 1-1 draw.