After the tourists were left with a target of 262 off a minimum off 60 overs, Vandort dropped anchor to see his side home with an innings lasting nearly four hours and featuring 10 fours.
Experienced wicket-keeper Kumar Sangakkara made 48 and Chamara Kapugedera helped see Sri Lanka home with an unbeaten 44 off 45 balls.
At tea, the Sri Lankans were 127-1, needing another 135 from 31 overs, and Sangakkara danced down the pitch to the second ball after the break from seamer Mo Sheikh.
But he was stumped attempting a repeat off Andy Gray but Vandort and Kapugedera prevented further trouble after Tillakaratne Dilshan went cheaply.
Sri Lanka conclude their first Test preparations with a four-day match against England A starting at New Road, Worcester, on Thursday.