The left-hander was batting on 104 at lunch on Tuesday, the third day with Jason Gillespie on 24 in a team score of 226-7.
Gilchrist, 51 overnight in a score of 145-6, had so far struck 12 boundaries and two sixes in his defiant innings and his unbroken stand with Gillespie was worth 70 valuable runs.
Gilchrist, who on Monday passed 5,000 runs in Tests, helped Australia to wriggle out of an embarrassing position as Bangladesh have never managed to give a follow-on to any team since gaining Test status in 2000.
The 34-year-old completed his 16th ton in 84 Tests with a drive through the covers off part-time spinner Rajin Saleh. He showed full confidence in his partner Gillespie and did not try keeping the strike.
Earlier, Gilchrist's overnight partner Brett Lee (15) departed adding just two runs to his overnight score when paceman Mashrafe bin Mortaza trapped him leg-before.
The second and final Test will be held in Chittagong from Sunday. The Test series will be followed by a three-match One-day series.