Joseph's goals gave St. Lucia a 4-2 victory, matching Aruba's home leg win on Friday, forcing extra time and then the tiebreaker, where it prevailed 5-4.
It is the third straight World Cup qualifying campaign that St. Lucia, which first entered the competition for the 1994 championship in the United States, has advanced past the initial phase of qualifying.
Joseph scored twice to put St. Lucia ahead 2-0 by the 29th minute. Frederic Gomez, who scored twice in Aruba's victory on Friday, pulled his side within one a minute before halftime, but Joseph restored St. Lucia's two-goal edge in the 71st and Kurt Frederick hiked the lead to 4-1 three minutes later.
Rensy Barradas scored in the 76th to deadlock the aggregate at 6-6, requiring the extra period and penalties, where Zane Pierre, Nathan Justin, Frederick, Kevin Edward and Pernal Williams all converted their attempts before Jelano Cruden was unable to with Aruba's last try.
St. Lucia will join Bermuda, Bahamas, the U.S. Virgin Islands and the Dominican Republic in the World Cup qualifying draw on July 30 in Rio de Janeiro. The sides will be draw with 19 other teams into six, four-team groups, the winners of which will advance to the semifinal round of CONCACAF qualifying.
One preliminary round series is still pending. Belize, which beat Montserrat 5-2 in the first leg of their series in Couva, Trinidad, will host its "home leg" on Sunday in San Pedro Sula, Honduras.