The world number three faced a tough test against his Russian opponent as Kudryavtsev continued to hold his serve right until the end of the first set, which almost led to a tie break.
Federer prevented prolonging the opening set by clinching the lead seven games to five in a thrilling early stage of the match.
The Russian 26-year-old refused to back down at the start of the second set, but failed to secure his first break of the game as Federer claimed a 2-1 lead with each game going by serve.
Before play could resume Kudryavtsev enlisted the help of his medical team to help relieve what appeared to be a groin injury. However, the Russian continued with the match but lost his serve as Federer stamped his authority to take the advantage in Melbourne.
The 16-time grand slam winner took control of the clash and managed to comfortably claim the second set six games to two, leaving Kudryavtsev with a mountain to climb.
The Russian claimed his first break of the match in the third set but failed to capitalise as Federer eased through the contest to progress in Melbourne.
The Swiss pro will meet either Eric Prodon or Andreas Beck in the next round.