New Zealand, who won the series 4-2, never recovered from losing early wickets in their chase and were all out for 253 in the 46th over.
The hosts were reduced to 42-3 in the 12th over and barring a 74-run stand between Luke Ronchi (47) and Daniel Vettori (35) for the seventh wicket, Sri Lanka always looked in control.
Kane Williamson top-scored for New Zealand with 54 while Kyle Mills hit a 17-ball 30 towards the end.
The 37-year-old Sangakkara, who is expected to retire from international cricket after the World Cup, passed Adam Gilchrist as the most successful wicketkeeper when he caught Corey Anderson off the bowling of Shaminda Eranga.
He later added another catch to the tally when he pouched Tim Southee off Thisara Perera, taking his career total to 474 dismissals with 378 catches and 96 stumpings in the 50-over format when he played as a wicketkeeper.
Australia’s Gilchrist achieved 472 dismissals in 287 one-day matches.
“The entire team has been working very hard. The hard work has paid off with some good performances out in the middle,” man-of-the-match Sangakkara said at the presentation.
“I just try to do the basics as well as I can.”
Earlier, Tillakaratne Dilshan (81) and Lahiru Thirimanne (30) gave Sri Lanka a good start, adding 71 for the opening wicket before the latter fell leg before to Anderson.
Sangakkara walked out at number three and then added 104 for the second wicket before Dilshan was out caught by wicketkeeper Ronchi off paceman Southee.
Sri Lanka lost a few quick wickets but Sangakkara held the innings together and brought up his century with a crisp pull shot off Mitchell McClenaghan. The stylish left-hander hit 14 boundaries in his 105-ball knock.
Anderson finished with three wickets for 59 runs for New Zealand.
The World Cup, which is co-hosted by New Zealand and Australia, runs from Feb. 14-March 29.
(Reporting by Sudipto Ganguly in Mumbai; Editing by John O’Brien)