It was also Sri Lanka's first win in an ODI series over the Black Caps in 12 years.
Kusal, 29, struck a career-best 143 and Avishka hit 100 as Sri Lanka posted a commanding 324-5 in 49.2 overs before rain stopped play.
Ferguson was struck down with the injury soon after becoming his nation's sixth bowler to take a T20 hat-trick as New Zealand won by five runs in Dambulla on Sunday to split the series 1-1.
It was also Sri Lanka's first win in an ODI series over the Black Caps in 12 years.
Kusal, 29, struck a career-best 143 and Avishka hit 100 as Sri Lanka posted a commanding 324-5 in 49.2 overs before rain stopped play.
Ferguson was struck down with the injury soon after becoming his nation's sixth bowler to take a T20 hat-trick as New Zealand won by five runs in Dambulla on Sunday to split the series 1-1.
