Warner, determined to finish an undistinguished series on a high, reached his 16th Test century off 82 balls before a small Sydney crowd in the last rites to a frustrating Test.
The buccaneering opener had a highest score of 64 in the two previous Tests as team-mates helped themselves to six centuries against the tourists' innocuous bowling attack.
Warner was hell-bent on rectifying that inadequacy and attacked the bowling from the first ball to raise his maiden ton against the West Indies.
The match was consigned to a draw after two days were washed out with only 86.2 overs possible before the anti-climatic fifth day.
When play resumed, the West Indies added 82 runs before being dismissed for 330.
Australia, and Warner in particular, went after the tourists' total with gusto to entertain the small crowd given free admission into the Sydney Cricket Ground.
Warner provided plenty of entertainment, clubbing spinner Jomel Warrican for two sixes in three balls on the way to plundering 16 runs from one over.
The pair raised their 100-run stand off 92 balls, with Warner contributing 74 runs.
Burns was out soon after, attempting to hoist Warrican over mid-on only to be taken head-high by Kemar Roach for 26.
Under-used Mitchell Marsh and wicketkeeper Neville were promoted in the order.
Marsh, in only his third bat of the series, was caught at slip for 21 giving spinner Jomel Warrican his fifth wicket of the series and making him his side's leading wicket-taker over the three Tests.
Spinners Nathan Lyon and Steve O'Keefe each took three
wickets to finish off the first innings which had remained on hold since Monday after two days of unrelenting rain.
Wicketkeeper Denesh Ramdin pushed his score to 62 after the West Indies surprised by deciding to bat on and not declare.
Play finally got under way under sunny skies, just over 70 hours after the previous ball was bowled on Monday's second day.
Days three and four were totally washed out, making it the first time that two consecutive days had been lost to rain in a Test in Australia in almost 26 years.
The players wore black arm bands as a mark of respect for the father of West Indies batsman Rajendra Chandrika, who passed away this week.
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