However, Campbelle stroked a superb unbeaten 27 from 23 balls and Smartt got 12 from eight balls, as West Indies got home in the last over with five balls to spare.
The victory was the third straight for the hosts after they won the doubleheader at Kensington Oval in Barbados last week.
Winning the toss and batting, Sri Lanka got a top score of 22 not out from Deepika Rasangika as they reached 77 for eight.
They were pegged back by fast bowler Subrina Munroe (2-12), off-spinner Stafanie Taylor (2-16) and left-arm seamer Shanel Daley (2-17) all of whom took two wickets apiece.
Seamer Sripali Weerakkody (3-23) then stunned the hosts with a lethal opening burst with medium pacer Chamani Seneviratne (2-8) giving excellent support.
West Indies’ top batters fell cheaply, as Taylor went for 10, Deandra Dottin departed for a first-ball duck and Daley perished for five.
When Anisa Mohammed holed out in the deep trying to clear long-off in the 13th over, it seemed all over for West Indies.
But Campbelle and Smartt rallied the side in a stand that lasted just 17 balls before Smartt sealed the deal with an off-side boundary off the first ball of the final over.
SRI LANKA (16 overs)
C. Athaparththy c wkp. Aguilleira b Daley 7
P. Weerakody b Munroe 15
Y. Mendis c Mohammed b Munroe 6
D. Rasangika not out 22
S. Siriwandena c wkp. Aguilleira b Campbelle 12
C. Seneviratne c Nero b Mohammed 1
I. Galagedara b Taylor 2
S. Weerakoddy c King b Daley 0
D. Manodara lbw b Taylor 1
S. Dolawatta not out 4
Extras: (b-1, lb-1, w-5) 7
Total: (8 wkts, 16 overs) 77
Fall of wickets: 1-17, 2-29, 3-30, 4-56, 5-59, 6-64, 7-67, 8-68.
Bowling: Selman 2-0-7-0, Daley 4-0-17-2, Munroe 3-0-12-2, Mohammed 3-0-16-1, Taylor 3-0-16-2, Campbelle 1-0-7-1.
WEST INDIES (Target: 78 off 16 overs)
S. Taylor c & b Seneviratne 10
J. Nero c Seneviratne b S. Weerakoddy 7
D. Dottin c wkp. P.Weerakody b S.Weerakoddy 0
S. Daley c Rasangika b S. Weerakoddy 5
S. King lbw b Siriwandena 6
M. Aguilleira b Gunaratne 6
S. Campbelle not out 27
A. Mohammed c Siriwandena b Seneviratne 9
T. Smartt not out 12
Extras: (lb-2, w-1) 3
Total: (7 wkts, 15.1 overs) 80
Fall of wickets: 1-17, 2-17, 3-19, 4-23, 5-25, 6-38, 7-56.
Bowling: S Weerakoddy 4-0-23-3, Seneviratne 3-0-8-2, Siriwandena 3-1-8-1, Gunaratne 3-1-18-1, Dolawatta 2-0-21-0.