Barca dominated possession against the La Liga champions but Atletico defended stoutly and held the record Cup winners at bay until Juanfran fouled Spain team mate Sergio Busquets in the area six minutes from time.
Messi's effort from the spot was well saved by Atletico goalkeeper Jan Oblak, but the ball fell kindly for the Argentina captain and he tapped it into the net to give Barca the advantage ahead of next Wednesday's return in Madrid.
"It's a good result but the second leg is still to come and they are going to be 90 very intense minutes," Barca captain Andres Iniesta said in an interview with Spanish television broadcaster Canal Plus.
"We performed extremely well against an opponent which is very tough to overcome," added the Spain international.
"Not conceding a goal is an important achievement but it does not guarantee anything. We will try to do things well again in the return."
Villarreal or Getafe await in the last four and Villarreal gained the upper hand in their tie when captain Bruno Soriano, who had come off the bench half an hour earlier, curled in a free kick in the 85th minute at the Madrigal.
On the other side of the draw, Athletic Bilbao ground out a 0-0 stalemate at Malaga, while Sevilla play their first leg at Espanyol on Thursday.
After losing 3-1 at Barca in La Liga this month, Atletico produced a much improved defensive performance and were close to becoming only the second team to avoid conceding at the Nou Camp this season until Messi struck.
Luis Suarez, who has yet to spark since joining from Liverpool, had Barca’s best scoring opportunity in the first half when he was picked out by Ivan Rakitic in the 36th minute but he skewed his first-time shot over the crossbar.
Atletico restricted Messi, fresh from a hat-trick in Barca’s La Liga victory at Deportivo La Coruna at the weekend, to a single genuine chance when he also shot wildly over when well placed in the 12th minute.
The four-times World Player of the Year could have made it 2-0 in added time but fired a free kick from just outside the Atletico area narrowly over.
"It's a result that can be turned around," Atletico defender Miranda told Canal Plus.
"We have a good defence and we score in almost all our matches," added the Brazil international.
"With our fans behind us, who are always there when we need them, we will fight back."
(Writing by Iain Rogers, editing by Toby Davis/Patrick Johnston)
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