Koke's early goal for Atletico Madrid helped his side to a 1-0 win and knock Barcelona out of the Champions League with a 2-1 aggregate victory.
In the night's other quarter-final, holders Bayern Munich came alive in the second half after falling behind to beat Manchester United 3-1 and advance to their third straight Champions League semi-final.
Bayern advanced 4-2 on aggregate after a 1-1 draw in Manchester last week.
The German side dominated the first half but failed to make much out of its possession advantage, and Patrice Evra put United ahead with a superb volley in the 57th minute. The lead lasted only two minutes before Mario Mandzukic got the equaliser.
Thomas Mueller made it 2-1 in the 68th and Arjen Robben secured the victory in the 76th. United spent much of the game defending and waiting for counterattacks and that was not enough to eliminate the defending champion.
Adrian Lopez filled in for injured striker Diego Costa and created the fifth-minute opener for Atletico after finding the post, as the Atletico forward headed an ensuing cross on to Koke to fire home.
The boisterous atmosphere at the Vicente Calderon Stadium unsettled Barcelona early on, and Atletico striker David Villa hit the woodwork twice within the opening 20 minutes.
Barcelona dug in but produced few tangible scoring chances apart from a pair of first-half misses by Lionel Messi.
Atletico, which leads Barcelona by one point in the Spanish league, reached the last four of Europe's top competition for the first time since 1974.