West Indies lost the wicket of Brandon King (17) in 24 overs before stumps on Saturday and finished 1-58, still 491 runs behind. John Campbell was on 31 and Kavem Hodge 6 not out.
West Indies lead the two-match series after winning the first Test by an innings and 217 runs.
Dinusha and Mendis built on the foundation laid by Lahiru Udara and Kamindu Mendis whose record 215-run partnership had Sri Lanka 5-338 at stumps on the first day. Udara made 188 and Kamindu 84.
After taking two wickets late on day one and operating with the second new ball which was only two overs old, the West Indies wanted an early breakthrough on day two.Â
They were denied by Dinusha who made 92 and Mendis who made 69 and batted through all of the first and much of the second session.
Mendis was first to fall, to a relatively unthreatening delivery from Anderson Phillip which he tried to sweep and managed only to deflect onto his stumps.
Dinusha was out eight runs short of a maiden century, caught by King at cover off Hodge.
The tail then wagged. Prabath Jayasuriya made an unbeaten 17, Milan Rathnayake made 15 and Isitha Wijesundara 14 as Sri Lanka added 73 for the seventh, eighth and ninth wickets before declaring.
The West Indies pacers toiled hard and were sometimes let down by their fielders with John Campbell dropping a regulation catch of Mendis at first slip from the bowling Shamar Joseph.
