Sri Lanka were 288-4 in their second innings, a lead of 51 runs, when a sharp shower drove the players back to the pavilion as the groundstaff rushed out with the covers.
Thilan Samaraweera was unbeaten on 37 and Prasanna Jayawardene was on 13, hoping to deny Australia their second successive win in the series.
The tourists won the first Test in Galle by 125 runs.