In-form Llorente nets in Bilbao victory
In the late game, Sevilla surprisingly lost 2-0 at Sporting Gijon to end Gregorio Manzano's winning start at the helm of the Andalucian club.
The towering Llorente, in the Spain side for the injured Fernando Torres, netted three times in their recent Euro 2012 qualifiers to take his tally to seven goals in 12 games for the world and European champions.
Bilbao's Andoni Iraola had opened the scoring at San Mames after 11 minutes and Llorente doubled the lead with a trademark header.
Braulio pulled one back at the end for Zaragoza but their coach Jose Aurelio Gay remained under pressure as they slipped to the foot of the standings without a win this season.
Deportivo La Coruna are the only other team in La Liga without a win and they wasted a gilt-edged opportunity at home to Osasuna when they were held 0-0 despite the visitors playing almost an hour with 10 men.
Sevilla missed the chance to keep pace with the leading clubs when Argentine Gaston Sangoy and Diego Castro scored to hand Sporting the points at the Molinon.
Manzano replaced Antonio Alvarez three weeks ago and won his first two games in charge against Borussia Dortmund and Atletico Madrid, but Sangoy's impressive header rocked them back after just six minutes.
Sporting captain Castro made it 2-0 with a crafty backheel soon after the break to leave Sevilla, who had given unsettled Brazil striker Luis Fabiano a rare start, seventh with 11 points.
Levante won the battle of the promoted sides by beating Real Sociedad 2-1 at home, Racing Santander beat Almeria 1-0 with a goal from Pedro Munitis, and a Luis Garcia penalty gave Espanyol a 1-0 win at Real Mallorca.
Real Madrid top the standings after seven matches with 17 points from seven games, after their 4-1 victory at Malaga on Saturday.
Champions Barcelona are one point behind after beating early pace-setters Valencia 2-1.
Villarreal, with 15 points, can take first place if they rack up their sixth straight victory at promoted Hercules on Monday.