And they know they could find themselves four points adrift if Juve make the most of their game advantage against Atalanta on Wednesday night.
Paulo Dybala scored two goals for Juventus.
The 24-year-old Dybala continued his excellent run of form by curling a magnificent freekick into the top corner to give the hosts a 20th-minute lead. "All-in-all we can look forward to a great match".
Higuain should have doubled his side's lead after Dybala was fouled in the area by Gabriele Angella, but he saw his penalty saved by Udinese goalkeeper Albano Bizzarri shortly before halftime.
Inter arguably enjoyed the better chances after the restart too as Milan Skriniar almost put the hosts ahead, hitting the post with a header.
The visitors dominated possession in the closing stages, but couldn't break down Inter as their hopes of a first title since 1990 took another body blow.
The match started with a poignant tribute to Fiorentina captain Davide Astori following his tragic death.
Elsewhere, Ciro Immobile grabbed Champions League-chasing Lazio a 2-2 draw at Cagliari with an equalizer in the fifth minute of injury time.