Mendis walked at four and held on to his nerves as he delivered one of the most spectacular counterattacking hundreds in recent times.
Kusal Mendis remained unbeaten on 169* with Sri Lanka leading Australia by 196 runs at stumps on Day 3 in 1st Test at Pallekele.
Kusal Mendis added that his aim would be to tire the bowlers and score runs.
Sri Lanka's middle order batsmen Kusal Mendis and Niroshan Dickwella hit half-centuries against an Aaron Beard inspired Essex to guide in their first tour match in England.
Sri Lanka are scheduled to play the first game of the tournament against New Zealand.