Spain, having weathered early pressure from the Chileans, took the lead in the Group H decider when Villa curled a sublime ball into the empty net from 40 metres out on the left after goalkeeper Claudio Bravo had raced from his box to clear from Fernando Torres.
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Villa, who took his tally to 41 in 61 internationals, laid on the second when he took a pass to the left from Andres Iniesta and pulled the ball back into the middle where the midfielder shot low past central defender Waldo Ponce and Bravo.
Chile, playing on a knife edge in their efforts to impose Bielsa's attacking tactics and spar with Spain as equals, had midfielder Marco Estrada sent off in the 37th minute.
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The hard-tackling midfielder earned a second yellow card for a trip on Torres off the ball in the build up to Iniesta's goal, putting the South Americans at risk of a pasting in the second half.
However, coach Marcelo Bielsa, facing possible elimination for his side, made two bold half time substitutions and one of them, midfielder Rodrigo Millar, chipped over Iker Casillas to pull a goal back just two minutes after the resumption.
Spain plugged away looking for further goals but the hard working Chileans kept them at bay, protecting a goal that ensured they would go through in second place in Group H on goal difference even if Switzerland managed to beat Honduras. The Swiss were in fact held 0-0 by the group's whipping boys.
TIGHT GROUP
Vicente del Bosque's European champions also became protective of their lead going into the final quarter as they shared six points with Chile at that point and the Swiss could also potentially finish on six with tight goal difference coming into play.
Spain, by winning the group having started out with a shock 1-0 defeat by Switzerland, go on to meet Portugal in the second round, avoiding favourites Brazil, who won Group G.
"The defeat against Switzerland really made things difficult for us ... if we had drawn that match I think the whole group would have taken on a different look," Del Bosque said.
"I think the doubts did start to enter in when Chile scored, the players started to play more cautiously ... but we achieved our goal."
The tiring Chileans withdrew into their half but Spain gradually reduced their efforts to score a third goal and had long spells passing the ball across the back of their defence close to the halfway line as the clock wound down.
This contrasted dramatically with the action-packed first half in which Chile defenders Gary Medel and Ponce picked up yellow cards along with Estrada, while Spain go through to their next match free of bookings.
