The first opportunity came in the 13th minute when Antonio Rukavina drove into the box and forced a save from Miguel Moya. The resulting corner was swung in for Javi Guerra, but the striker headed over from close range.
Guerra then brought a spectacular save from Moya in the 33rd minute as the home side once again threatened to break the deadlock.
The teams went in level at the break but the hosts were ahead minutes after the restart, with Valiente finally beating Moya with a header.
Zakara Bergdich had a good opportunity to give his team some breathing space in the 55th minute but the 24-year-old saw his effort miss narrowly.
Hearts were in mouths for the home fans when Lafita sprung the offside trap two minutes later, but the winger fire wide of the target.
The 29-year-old Spaniard wasted another gilt-edged chance in the 78th minute which should have levelled the score.