Wings DTH van der Merwe and Sean Maitland, the latter off the bench, both touched down as Glasgow ended the RaboDirect PRO12 regular season, with a 20-3 victory on the road at Connacht.
With Ulster and Leinster both winning, the Warriors remained in third place in the table with a trip back to Ireland to face the latter at the RDS in the second of the two semi-finals on Saturday.
Glasgow lost to Leinster both home and away during the regular season but Horne admits spirits are soaring in the Warriors camp with the team full of belief that they can get a result in Ireland.
"I think confidence is high" Horne told the Scotsman. "We were delighted to tough out that win in Connacht after getting smashed by the Scarlets.
"We know that we will have to play some rugby to beat Leinster but our fundamentals, defence and discipline, are better than they were last season and our back three are on fire.
"All I have to do is pass them the ball and let them get their strut on."
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