The March 15 votes in both parties were extremely close: Clinton and rival Bernie Sanders were neck-and-neck, as were Trump and Senator Ted Cruz.
Missouri Secretary of State Jason Kander finally certified the result, tweeting: "@HillaryClinton and @realDonaldTrump have officially won Missouri."
Clinton earned 49.6 percent of the vote, to 49.36 percent for Sanders -- a margin of 1,574 votes, according to the results posted on the secretary of state's website. Each takes 34 delegates. On the Republican side, Trump earned 40.84 percent of the vote, to 40.63 percent for Cruz -- a difference of 1,965 votes.
The real estate mogul thereby takes 25 delegates to 15 for the Texas senator. Clinton and Trump are leading in the race to secure their respective party nominations ahead of election day in November.
The next primaries are set to take place on April 19 in New York. Clinton and Trump are both leading in opinion polls.