Celtic remained on course for a domestic treble after Jota's first-half header proved the difference in a 1-0 Scottish Cup semi-final win over arch Glasgow rivals Rangers at Hampden Park on Sunday.

The Hoops, runaway leaders of the Scottish Premiership, have already defeated Rangers in this season's Scottish League Cup final.

And they will be overwhelming favourites when they return to Hampden for the Scottish Cup final against second-tier Inverness on June 3.

Portuguese star Jota scored the only goal of Sunday's match three minutes before half-time  when he punished careless defending by heading in past goalkeeper Allan McGregor.

Borna Barisic and several other Rangers players stopped, anticipating a foul near the edge of the penalty area, and that allowed Japan's Daizen Maeda to steal in and whip the ball across goal. 

Jota could hardly miss with the close-range header after stealing away from Rangers captain James Tavernier. 

Cup-holders Rangers had several chances to equalise, however, with Tavernier hitting the post in the second half and Fashion Sakala missing an open goal from the rebound.

Their failure to make the most of their opportunities meant Celtic gained a measure of revenge for their semi-final defeat by Rangers last season.

"It's a semi-final, there's a big prize at the end so we knew it wouldn't be easy," Celtic manager Ange Postecoglou told the BBC.

"Dare I say it, we never stop. We're always alert. We force the opposition into mistakes.

"The progress we've made has been immense. It's credit to everyone involved."

Sunday's result meant Michael Beale has not beaten Celtic in four attempts since taking over as Rangers manager last November, while Rangers have not won an Old Firm game in six attempts.

"We shot ourselves in the foot again," said Beale. "We kept Allan (McGregor) pretty much safe the whole game.

"We've made a big mistake in a huge game. It's a repeat of what's happened. Right now, it's massive disappointment. When our opportunities came, we weren't able to take them."