Both teams already had been eliminated from semifinal contention with losses to Canada and Mexico in their previous two games.
After a pair of two-goal defeats (2-1 to Mexico and 2-0 to Canada), Jamaica had the better of play, especially until Jeune's ejection, but seemed unable to exploit the extra player advantage.
The "Reggae Girlz" had their best chances in the first half, a free kick by Trudi Carter from 25 meters that Haiti keeper Cynthia Chery had to tip over the bar in the 25th, and a volleyed effort by Kimberly Spence in the 32nd that Chery blocked and then had to be cleared off the line by Roselord Borgella when Spence tried to toe-poke the rebound.
Haiti, beaten 15-0 in its previous games (5-0 by Canada and 10-0 by Mexico) largely was restricted to long-range efforts, typified by Borgella's 30-meter free kick that Jamaica keeper Sashgay Spence handled with ease.
With both teams playing their third game in five days and temperate again in the 88-degree Fahrenheit (31 Celsius) range with 55 percent humidity, Jamaica appeared to gain a critical advantage when Surinamese referee Deborah Zebedah ejected Jeune for a shove and then stepping on Carter just outside the Haitian penalty area.
Haiti had surrendered 12 of 15 goals against Canada and Mexico in the second half.
But Jamaica only managed one serious effort over the next 25 minutes, a shot by Alika Keene from inside the penalty area that was wide of the near post in the 66th.
Shenika Williams was able get an unchallenged shot from the middle of the area in the 79th, but it was blocked in front. Khaidija Shaw had a late effort from distance that Chery punched wide.
Haiti even created its best opportunity in the 86th, a header from eight meters by Yvrose Gervil off Yolande Merone's corner that was directly at Spence.
The game was a rematch of Caribbean qualifier in the Dominican Republic on January 6, won by Haiti 1-0. It was the only game in five that Jamaica lost in qualifying.