Brad Patton provided the heroics with an undefeated century.
The 29-year-old left-hander, in just his fourth first-class match, notched up his second century, his 110 coming off 168 balls and including 11 fours and one six.
The match was evenly poised after the third day with Otago resuming its second innings on 211 for six, after conceding a first-innings deficit of just 21 runs.
But the visitors added just a further 70 runs, leaving Central needing 261 from a minimum of 73 overs.
Otago wicketkeeper-batsman Derek de Boorder resumed on 43 and carried his bat to finish the innings on 73, tantalisingly close to his highest first-class score of 74.
But wickets fell regularly at the other end, and once Ian Butler was dispatched by Jacob Oram for 27 with the total on 244, Doug Bracewell, son of former New Zealand cricketer Brendon, mopped up the tail with minimum fuss.
Bracewell's useful medium-pace collected three wickets for 51 off 10.4 overs as the last three wickets fell for 37 runs, leaving Otago with a total it was always going to struggle to defend.
Central's openers, George Worker and Peter Ingram, put on 59 for the first wicket before Worker departed, bowled by Butler for 28.
Central captain Mathew Sinclair came to the wicket with the score on 120 after Ingram was caught behind by de Boorder on 40, and settled in with Patton to secure the outright win.
Fittingly, the winning runs came from Patton's bat as he slashed an emphatic four to third man off the bowling of Neil Broom.
Sinclair was 52 not out.
