Eric Bristow achieved the feat twice in the 1980s and Barneveld wrote his name into darts history when he beat Baxter 6-5 in a tie-break final set that the Dutchman finally won by four legs to two.
Baxter, from Church, Lancashire, led 5-4 but Barneveld won the 10th set in three straight legs and looked set to coast home when he won the first two legs of the final set.
Then, in the fourth leg, Barneveld had three chances to win the match but missed double 12 and then double six twice to give Baxter renewed hope.
Baxter recovered to two-legs all but Barneveld pulled himself together to win the next two legs, finally slotting double 16 on his fourth match dart to clinch the victory.
The final, which lasted only one hour and 41 minutes, was one of the tightest in Embassy history.