Woods, an avid Arsenal fan, was in a despondent mood after seeing the Gunners fall to a 2-0 defeat against Newcastle on Monday night, a result that will go down as a bitter blow in their pursuit of Champions League football.
As a result, Tottenham effectively need to avoid defeat against already-relegated Norwich in order to wrap up fourth spot once and for all.
Sat alongside fellow Arsenal fan Darren Bent, Woods was taking calls from fans when a call came through from a Tottenham supporter called 'James'… and it didn't take long for the talkSPORT host to uncover his identity.
Spurs fan 'James': *Laughs maniacally*
Woods (laughing): "Cut him off immediately!"
Spurs fan 'James': "Howay the lads! Howay the lads!"
Woods: "Ah… you know what… that's Jamie O'Hara isn't it? What are you guys doing to me?!"
O'Hara (singing): "Arsenal get battered everywhere they go. Arsenal get battered, everywhere they go! Morning Woodsy!"
Woods: "You are unbearable. You are unbearable at the best of times! I'm going to say one thing, do not count your chickens too early, Jamie O'Hara."
O'Hara: "It's over, Laura. It's over! We only need a point, you've absolutely bottled it! I told you. Your rallying cry, everything you said to me yesterday on the call went down in flames. They absolutely crumbled. I just went into Tesco to get some apple crumble and they didn't have any because Arsenal took it all! It's a shambles!"
Woods: "This is dreadful. Did you write all of these lines down before you came on? He's literally got them all written down. Did you stay up all night, Jamie?"
O'Hara: "I love it. I can't believe we've got two Arsenal fans on. Absolutely amazing."
Woods: "Brilliant. Like my morning couldn't get any worse, Jamie O'Hara on talkSPORT Breakfast has just pushed me over the edge."
After calming himself down, O'Hara went on to explain that while Arsenal finishing the Premier League season in fifth is progress, there's no doubt that Mikel Arteta's players will see it as 'failure' considering how close they've come.
He said: "I told you yesterday that Arsenal were going to crumble. In the north London derby they had absolutely nothing to show. Last night, Newcastle played like a Champions League club.
"Alright, if Arsenal finish fifth it hasn't been a disaster of a season.
"I would say it's progression, but when you look at what they've spent, the fact they haven't had European football and the fact that they had two games left and the Champions League was in their destiny and they've thrown it away, I think the players will say they've failed.
"Whether over the whole course of next season you've got the Europa League, alright. It's not Champions League, but it's still European football and you'd say well done.
"But the players and the manager will be sat there at the end of the season and will 100 per cent think they've failed."
Responding to Woods' comment that no one expected to finish in the top four, O'Hara added: "No, but they're not going to be in the top four. I said Europa League football and that's where they've finished.
"Granit Xhaka last night, come one. He comes out, digging out the players. Has he forgot that he got sent off how many times this and cost his team with them running around for however many minutes with 10 men, and he's got the cheek to say 'if you can't handle the pressure then don't bother turning up'? That is a joke.
"If you talk about leaders, they got rid of Pierre-Emerick Aubameyang who has banged in how many goals for Barcelona?
"He's gone to LaLiga and done it, so Arteta's done something wrong.
"At the end of the day, the last two games have been nowhere near good enough. You can get beat, but the manner of those two defeats, Arsenal fans will be absolutely seething.
"They haven't showed up in a north London derby and then in Newcastle when it was still in your hands to qualify for the Champions League and you absolutely folded like a deck of cards.
"It's embarrassing."