The Hammers remain in the hunt for a Champions League place, but are some way behind Arsene Wenger's third-placed side.
The Hammers' top-four chase has stalled over the past two matches, with controversial refereeing decisions arguably costing them maximum points.
The in-form Gunners, who hold a seven-point advantage over Slaven Bilic's team, are the visitors to Upton Park tomorrow but Gabbidon thinks they'll come unstuck on the other side of the capital.
"I'm going to go with a West Ham win," the Welshman told the Hawksbee and Jacobs show on Friday.
"I think maybe two of their last couple of games refereeing decisions have gone against them.
"They're pushing for the top four, I think they're due a bit of luck - I'm going to go with a 2-1 win for West Ham."
West Ham squandered a 2-1 lead to draw 2-2 with Chelsea at Stamford Bridge three weeks ago, after Michail Antonio tripped Ruben Loftus-Cheek outside the area, but a penalty was awarded by referee Robert Madley.
And the Hammers were left bemoaning the officials once more on Saturday, with Crystal Palace leaving the Boleyn with a point after Cheikhou Kouyate was controversially dismissed by Mark Clattenburg with the score 2-1.
The Senegal midfielder has since had his red card rescinded, although a number of ex referees have questioned the decision.