The win helped the Golden Eagles (26-13, 6-6 in Conference USA) avoid the series sweep against the Green Wave, 27-12-1, 6-5-1).
It also marked Palmer's first regular season win at Tulane since the 2000 season, which also came in the final game of a three-game series.
This win, however, came in spite of five Golden Eagles errors and a mere five hits.
"I would rather get an ugly win than a pretty loss," Palmer said. "This is a tough place to play and this may have broken a little of the ice. But it was ugly."
Of the five hits, three were home runs, including a solo shot by Michael Ewing in the second, a two-run blast by Drew Carson in the third, and a three-run homer by Chris Matesich in the fourth.
"That (the home runs) is the reason we won," Palmer said. "But we did have one terrible inning defensively."
The inning Palmer spoke of was the bottom of the third with the Golden Eagles leading 3-2 after Carson's eighth home run of the season.
Facing Southern Miss starter Houston Brown, Tulane scored three unearned runs off three Golden Eagles errors - two by catcher Kyle Maxie - and one passed ball.
The inning started with a walk to Drew Allain, the Green Wave's No. 9 hitter. After a fly out by Aja Barto, Anthony Scelfo singled to right and later took second on a passed ball. Seth Henry then hit a routine grounder to Matesich at third base, who threw home to get Allain in a run down.
Maxie's run down throw back to third in the run down sailed into the left field, allowing Allain to score.
Drew Carson's return throw home was up the first-base line, which allowed Scelfo to score for a 4-3 lead.
With two outs, and Tulane leading 5-3, Maxie missed a fly out near home plate off the bat of Andrew Rogers. Instead of being down two runs, Southern Miss saw Rogers hit the next pitch out of the park for a 6-3 lead.
Southern Miss, which lost 4-3 and 4-2 in the first two games of the series, battled back to tie the game at 6-6 in the fourth on a three-run home run by Matesich.
Once again, the lead was short-lived.
Tulane grabbed a 7-6 lead off two more Southern Miss errors. The big error came when relief pitcher Collin Cargill pickoff attempt to first sailed high, scoring Sam Honeck from third.
Southern Miss took control in the fifth inning with four runs off one hit, one sacrifice fly by Carson - only the sixth of the season for the Golden Eagles - and one Green Wave error.
"We would have loved to get the series win," Matesich said. "Getting one win was better than zero. It was ugly, but we will take it."
Tyler Conn, a senior from Ocean Springs picked up his school record 14th save despite allowing his first earned run of the season with 22/3 innings of work. Collin Cargill improved to 3-0 win the win.
"I had nothing," Conn said. "I had no fastball. I had no changeup. I just kept telling myself that I had to get it done."
When: Tuesday and Wednesday, 6:30 p.m.
Where: Pete Taylor Park, Hattiesburg