The big-serving Ljubicic, seeded 20th, fired down 20 aces and hit 42 winners to seal an emotional victory in two hours seven minutes on the stadium court at the Indian Wells Tennis Garden.
Appearing in his fourth Masters final, the 31-year-old clinched the second-set tiebreak 7-5 after unleashing a booming service winner before thrusting both arms skywards.
Ljubicic then removed his sweatband before walking to the net to shake hands with Roddick who had saved three match points in the tiebreak after clawing his way back from 5-1 down.
“It’s been a fantastic week,” Ljubicic said at courtside after winning his 10th ATP title.
He had played some of the best tennis of his career at Indian Wells, eliminating second seed Novak Djokovic in the fourth round and third seed Rafa Nadal in the semi-finals.
He maintained that form in yesterday’s final with an all-round power game shrewdly mixed with clever angles and deft touches at the net.