Federer, 36, becomes only the fourth player after Margaret Court, Serena Williams and Steffi Graf to win 20 or more major singles titles.
The final was played under the Rod Laver Arena roof as the tournament's extreme heat policy was invoked.
Despite starting at 19:30 local time in Melbourne, the conditions were if anything more testing than 24 hours earlier, when Caroline Wozniacki and Simona Halep played to the point of exhaustion in the women's final.
With the roof closed and air-conditioning taking the edge off the temperature, Federer and Cilic played out a gripping contest over three hours and two minutes.
After a poor start, Cilic looked to have the momentum when he won five games in a row to force a fifth set, but Federer clung on to his serve at the start of the decider and got the key break in the following game.
The Swiss ties the record for men's Australian Open titles at six with Novak Djokovic and Roy Emerson, and moves four clear of Rafael Nadal in the all-time list for male Grand Slam champions on 20.
credit: BBC