John Walker III scored 14 points and Davon Barnes 13 for Texas Southern (14-20) which clinched its third straight SWAC postseason conference tournament and became the first SWAC eighth seed to win the tournament.
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Reserve Zahad Munford scored 12 points for Grambling (24-9), Jonathan Aku scored 11 points and grabbed 10 rebounds and Tramichael Morton scored 10.
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Henry started 1-for-13 shooting before going on a 4-for-4 stretch - which included three 3-pointers - to help put an end to Grambling's rally. His 3 with 6:08 left broke a 43-all tie and Texas Southern led for the remainder. Grambling needed a 14-3 run to forge the tie.
Grambling played catchup all day and didn't score a field goal until a little more than 6 1/2 minutes in when Cameron Christon reduced the deficit to 13-4.
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Texas Southern finished the regular season with three straight losses before ending the skid with an opening-round win over top-seeded Alcorn State, then beat No. 5-seed Alabama A&M in the semis.
Grambling was the No. 2 seed. It was Texas Southern's eighth trip to the SWAC championship game in the last nine years.
The loss was a disappointing end for Grambling which set a season program record in wins and entered with an 11-game win streak.
The Tigers went 2-1 against Power 5 opposition, including a 64-62 win at Vanderbilt which lost in the SEC tournament semifinals earlier in the day.
The Associated Press contributed to this report.