Rangers moved level on points with cinch Premiership leaders Celtic with a 3-1 win over Ross County but their profligacy prevented them going top.
The Light Blues took the lead in the fifth minute through striker Cyriel Dessers and the home side then hit the woodwork twice amid an onslaught.
However, the second-bottom Staggies, with Don Cowie in charge for the first time following the departure of Derek Adams last week, unexpectedly levelled in the 25th minute with a Simon Murray strike.
Dessers grabbed his second in first-half added time to placate the Gers fans frustrated at the missed chances but there were more opportunities passed up in the second half before defender John Souttar eventually headed in a third late on.
After eventually catching up on fixtures with Celtic, the Govan side are level on points and goal difference with the Hoops but have scored four fewer than their Old Firm rivals.
Another huge crowd rolled up to Ibrox knowing a three-goal win against a club who had never beaten Rangers in 23 attempts would see the lead at the top change hands.
Philippe Clement made seven changes from Saturday’s 2-0 Scottish Gas Scottish Cup win over Ayr United.
Ridvan Yilmaz, John Lundstram, Tom Lawrence, Ross McCausland, Todd Cantwell, Rabbi Matondo and Dessers all returned while Cowie brought in Eamonn Brophy, Michee Efete, Ryan Leak, Josh Reid and Victor Loturi.
A sense of expectancy hung heavy in the air.
Dessers struck early, taking a pass from captain James Tavernier and fending off the attention of defender Leak before lobbing the ball over stranded Staggies keeper George Wickens and the Light Blues were up and running.
Wickens soon had to tip a powerful shot from Tavernier past the post for a corner, which the startled Dingwall side survived.
In the 10th minute Dessers latched on to a raking pass from left-back Yilmaz and beat Wickens only to see the ball rebound off the post.
Then Matondo raced onto a defence-splitting pass from midfielder Lundstram and curled the ball past the far post before Wickens tipped a shot from the wide man onto the bar and over.
Lawrence, Souttar, Tavernier and Dessers had further efforts of various quality before Murray stunned the home fans into silence with a confident volley from six yards from a delicious Brophy cross.
The mood inside the stadium darkened.
The Gers crowd looked on in astonishment as Leak stopped Dessers’ close-range shot after Wickens had spilled a Cantwell drive but the enigmatic striker made up for it by heading in a Tavernier cross seconds before the break which changed the atmosphere again.
January signing Oscar Cortes, the 20-year-old Colombian signed on loan from Lens, replaced Matondo at half-time and in the 52nd minute had a decent drive parried clear by the over-worked Wickens, who soon tipped a long-ranger from Cantwell past the post.
The pressure on the County goal was relentless but just after the hour-mark the Gers fans were relieved to see Efete head a County corner over the bar when he should have worked keeper Jack Butland.
Wickens made further saves from Lundstram, Lawrence and Dessers before the latter was replaced by Portuguese striker Fabio Silva.
In the 74th minute Cortes missed the target from 12 yards and, amid a myriad of attempts on the County goal, Wickens denied Cantwell and Cortes again.
But in the second of seven added minutes Souttar headed in a Tavernier cross but there was to be no later drama and the chance to strike a psychological blow was gone.
Terzic: Dortmund have made up for last season's Bundesliga failure
Borussia Dortmund's 2-0 aggregate win over Paris Saint-Germain made amends for last season's disappointing Bundesliga finale, coach Edin Terzic said.
Dortmund showed great composure to reach their third Champions League final and first since 2013 after Mats Hummels' second-half goal earned a 1-0 victory on the night in Paris on Tuesday.
Terzic went to the Dortmund fans after the game and said he felt he had to make up for last season's failure to win the Bundesliga title after slipping up on the very last day.
"Last season, we lost the championship at home on the last matchday. I'm happy that we can now give something back to the fans," Terzic said, remembering how Bayern Munich snatched the Bundesliga title from Dortmund on goal difference.
"[Going to the fans] was a very emotional moment, a beautiful moment. We wished it for last season's last matchday. But today we could pay something back, keep them dreaming and now we'll do everything to bring the trophy back home," he said.
PSG hit the woodwork four times but failed to find the net as Kylian Mbappe, widely expected to leave at the end of the season, was a shadow of his usual brilliant self.
Dortmund will now meet either 14-time European champions Real Madrid or their Bundesliga rivals Bayern in the June 1 showdown at Wembley.
"Before the first game against PSV, we talked for the first time about how short the journey to London could be," Terzic said.
"Back then, many were still puzzled. We've grown with every game and eventually realised that we could be the team that surprises everyone in the end. Now I'm very happy to be in the final with my team."
Dortmund have played a roller-coaster Bundesliga season and sit in fifth place with two games left.
"That plays no role," Terzic said. "In 2013 when Dortmund were in the Champions League final they were 25 points behind in the league and in 1997 when they won it they were also not doing well.
"The season had highs and lows but our season is still not finished."
'I don't see why we shouldn't win' - BVB hero Hummels bullish ahead of Champions League final
Mats Hummels sees no reason why Borussia Dortmund cannot go on and win the Champions League following their hard-earned semi-final victory over Paris Saint-Germain.
The Black and Yellow are through to the final of Europe's premier club competition for only the third time after sealing a 2-0 aggregate over the reigning Ligue 1 champions, who struck the woodwork six times across both legs.
After Niclas Fullkrug settled last week's first leg at Signal Iduna Park, Hummels' second-half header was the difference in the return at Parc des Princes, where Edin Terzic's side produced another defensive masterclass as they claimed their sixth clean sheet in this season's competition.
Dortmund, who lifted the trophy 27 years ago, will face either Real Madrid or Bayern Munich in the final at Wembley on June 1, and Hummels is confident he and his team-mates can go all the way.
"I've scored far too few Champions League goals in my career, just five," he told DAZN via Uefa.com. "Now is a good time to add to that number.
"Since the second match of the group stage, we've believed that we could prevail in every game - and I don't see why we shouldn't win at Wembley now.
"We remained active today and were able to take so much pace out of the game and atmosphere out of the stadium. That was our recipe for success today."
Hummels was part of the Dortmund side beaten 2-1 by Bayern in their most recent Champions League final appearance in 2013, along with Marco Reus.
The veteran midfielder announced last week that he would be leaving the club at the end of this season, and is thrilled to have one more crack at landing the biggest trophy in European club football.
"[It is] indescribable," he told DAZN. "After more than 10 years, I am in the final with Borussia again. Ousmane [Dembele] and Achraf [Hakimi] brought a tremendous amount of pace, and we suffered a lot.
"How we won the game, no-one will ask tomorrow. Shots against the post won’t matter tomorrow. What counts is that Borussia Dortmund are in the final again. Nobody expected this. It's just incredible."
Meanwhile Terzic, who saw his side surrender the Bundesliga title on the final day of last season, saluted the strides his players have made as the competition has progressed.
"Before the first game against PSV [in the round of 16], we talked for the first time about how short the journey to London could be," he said. "Back then, many were still puzzled. Last season, we lost the championship at home on the last matchday.
"I'm happy that we can now give something back to the fans. We've grown with every game and eventually realised that we could be the team that surprises everyone in the end. Now, I'm very happy to be in the final with my team."
'We weren't efficient' - Marquinhos bemoans PSG profligacy after Champions League exit
Marquinhos believes Paris Saint-Germain paid for their profligacy after suffering Champions League semi-final heartbreak against Borussia Dortmund.
Mats Hummels' second-half header from a Julian Brandt corner - the only goal at Parc des Princes - wrapped up a 2-0 aggregate victory for the Bundesliga side, who advanced to their third final and first since 2013.
Meanwhile, PSG's wait to land the elusive European crown goes on, despite a whopping 44 shots across the two legs, while they also struck the woodwork on six occasions - their overall tally of 14 the most recorded by a team during a single campaign.
Indeed, Luis Enrique's side failed to find the net in a home match for the first time since their 0-0 draw with Lorient in their first Ligue 1 match of the season, as their hopes of completing the treble vanished for another year.
"We lacked efficiency," Marquinhos told Canal+. "They scored two goals from corners and a through ball that we had worked on. We had to defend better. These are small details.
"We created chances, a lot more than them. We weren't efficient. They were efficient, they scored two goals and won both matches."
But despite the disappointment, the PSG skipper urged his team-mates to focus on the positives from their run to the semi-finals.
They recovered from a disappointing 4-1 defeat against Newcastle United to finish second behind Dortmund in Group F, before overturning a 4-2 aggregate deficit to deny Barcelona in the quarter-finals.
"There are a lot of things to take away from this competition," Marquinhos added. "At the beginning of the season, no one believed that we would get this far. We've overcome a lot of obstacles, we shouldn't throw everything away now just because we're eliminated.
"You have to remember that it's a new team, with a new coach. There are some positives to bring back for next season. We wanted to go to Wembley for the fans and our families.
"You have to stay calm after the elimination. It's very hard. We've come very close. We had to win tonight and be more efficient."
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