Jackson finished first in Alaska's Democratic precinct caucuses, posting a narrow victory over Dukakis in a non-binding preference poll announced Friday.
With about 90% of Alaska's 442 precincts reporting from the Thursday night meetings, Jackson had 872 votes, or 35% of the total, to Dukakis' 769 votes, or 31%.
A close third was "uncommitted," with 768 votes, or 31%.
Gore, Simon and Missouri Rep. Richard A. Gephardt divided the remaining 3% of the votes.
No major Democratic candidate campaigned in Alaska, and only Dukakis and Jackson had active organizations.
Henry Lancaster, statewide coordinator for the Jackson campaign, said that with blacks making up just 3% of Alaska's population, his candidate's appeal came as a result of the anti-drug and economic issues Jackson has been voicing around the nation.
Alaska Democrats will send 17 delegates to the Democratic convention in July. Twelve delegates will be picked at a state convention in May, which concludes a three-tier process that began with Thursday's caucuses. The other five delegates will be elected state officials.