Ebdon took the opening frame on the black, lost the second in similar circumstances and then edged a tactical third to move 2-1 in front.
Trump, the UK champion, levelled for a second time with a 131 total clearance and forged ahead with a contribution of 90 in the next.
And he finished off the comeback with breaks of 27 and 47 in the sixth and deciding frame.
In the opening match of the night, Stuart Bingham beat Ding Junhui 4-2 for his first win of the campaign.
The Englishman opened with a 75 and added a scrappy second frame before Ding drew level at 2-2 thanks to runs of 54, 38 and 73.
But Bingham rolled in breaks of 75 and 50 to close out a victory that moves him above Ding into second place in Group A.