The powerful Basque striker, who has an outside chance of making Vicente del Bosque's Spain squad for this year's World Cup finals, scored the first, set up the second and netted the third from the penalty spot at San Mames.
The 25-year-old crashed a header past Fabio Coltorti from a corner in the 13th minute, spun his marker to cross for Gaizka Toquero to stab in a second and almost made it 3-0 with an audacious backheel.
Mohamed Tchite pulled one back for north-coast rivals Racing just before the break, but Llorente converted a penalty in the 78th minute to spark a late flurry of activity.
Substitute Ivan Bolado scored with a spectacular overhead kick for Racing 10 minutes from time, but they lost defender Oriol Lozano to a red card for elbowing Llorente.
Markel Susaeta broke away to clinch victory for the hosts in the 87th but Bolado grabbed his second of the night in time added on from a wonderful Sergio Canales pass.
Bilbao strengthened their hold on sixth place, moving level on 45 points with fifth-placed Sevilla after 29 games.
Sevilla, fourth-placed Real Mallorca (47) and third-placed Valencia (53) all lost at the weekend.
Real Madrid top the standings with 74 points after their 3-2 derby win over Atletico Madrid at the Bernabeu. Barca are second on goal difference having beaten Mallorca 1-0 on Saturday.
