The seven-time champions paid the price of not creating enough chances and wasting those they got against a Sri Lankan side 98 places below them in the FIFA rankings.
Dhawan completed the landmark while his team was chasing a target of 263 at the R Premdasa Stadium.
The left-arm wrist-spinner took two key wickets in his nine overs in the first ODI on Sunday and gave away only 48 runs in a spell that should reinstate some of his lost confidence.
Laxman said Dhawan might be leading the side but he has to be amongst runs in the Sri Lanka series considering the stiff competition for the opening spot in T20 World Cup squad.
The Tamil Nadu batsman waved his bat to the stadium and later performed the iconic Griezmann move to celebrate his century.
The Indian captain scored 104 not out in Kolkata followed by 213 in Nagpur before completing his hat-trick with his 20th Test hundred in his 63rd game here.
Playing in his 63rd Test, the 29-year-old from Delhi became the 11th Indian batsman to achieve the milestone