Watch highlights of day four
Resuming on 22, Carberry pushed on to 125 on the final day before Glenn Maxwell’s 85 and Sean Ervine’s 42 not out saw the visitors through at 321 for five.
Worcestershire's Charlie Morris took three wickets but his side could not find sufficient penetration to force an unlikely victory in a match disrupted several times by wet weather.
The day began with Will Smith surprisingly walking out to the wicket rather than Danny Briggs, who had seen out two balls as nightwatchman on Tuesday night but was absent to be at the birth of his first child.
Smith made 11 in a stand of 35 with Carberry before being bowled by Morris.
— Hampshire Cricket (@hantscricket) June 11, 2014
That brought James Vince to the middle and he quickly went on the offensive, striking three boundaries in two Morris overs.
But he reached only 16 before being trapped lbw by Morris - though Maxwell too was swiftly into his stride, with four boundaries in the same Saeed Ajmal over taking him to 17 from eight balls.
Carberry hit Morris for four, his 10th as he reached a 106-ball half-century.
Maxwell was enjoying himself against Ajmal, blunting Worcestershire's most feared weapon, and hoisted the Pakistan spinner for six to end the 41st over.
Lunch arrived with Hampshire 147 for three, still 36 runs behind, and soon after the restart Maxwell reached a 40-ball half-century with a four off Ajmal.
— Worcestershire CCC (@WorcsCCC) June 11, 2014
Carberry moved into the nineties with his first six and followed up by hitting Ajmal for four before reaching his century from 192 balls, an innings which also featured 17 fours.
Maxwell hit a six and two fours in Ajmal's next two overs but was finally dismissed lbw by Morris, his 85 coming from only 87 balls with 11 fours and two maximums.
Carberry's final runs were a boundary off Ajmal before he became yet another lbw victim, giving Joe Leach his only wicket of the innings.
Ervine was on 17 at the time and pushed on in the company of Michael Bates before stumps were drawn shortly before 5.30pm. Worcestershire took 12 points to Hampshire's four, with the teams level on 118 points at the top of Division Two.