Bradshaw, who captained the Tribesmen in their 17-point mauling by Mayo last week, but who was sent off in the second-half, saw his club stunned by a late goal as Kilconly won by 2-12 to 2-9.
And it was also a red-letter day for former Galway star Padraic Joyce who was sent off when he picked up two yellow cards as Killererin were surprisingly defeated 2-10 to 0-8 by city side St Michael’s.
Joyce’s Killererin will now go into the losers’ group in Galway where they will be joined by reigning champions Salthill/Knocknacarra.
The holders were shocked by last year’s intermediate champions Carna/Cashel on a 2-6 to 0-11 scoreline.
A Seosamh Ó Cathasaigh’s goal in the opening half paved the way for Carna/Cashel, but Galway star Sean Armstrong was left to carry Salthill/Knocknacarra’s hopes. He scored all but one of the Salthill scores, with Gary Cox getting the other one. Ó Cathasaigh’s second goal for the Connemara side put them in the driving seat for a sensational win with Armstrong off target with a late chance to snatch a draw from distance.
Elsewhere, a Michael Meehan goal helped former All-Ireland champions Caltra defeat St James by 2-11 to 2-9, while former Kildare star James Kavanagh helped new club Milltown pip Caherlistrane by 1-10 to 1-9.
Corofin sent out a title warning with a facile win over Micheal Breathnachs.
Second-half goals from Alan O’Donovan and Galway U21 star Ian Burke set up an easy victory over the Connemara side, winning by 3-17 to 1-7. The game was as good as over at half time when Corofin led by 1-11 to 0-3.
A late goal from Michael Daly wasn’t enough to save Mountbellew/Moylough, who lost out to Naomh Anna/Leitir Móir on a scoreline of 2-14 to 2-11. Padraic Mark O Flaherta’s second-half goal put the Connemara side well in control and injury to Joe Bergin added to Mountbellew/Moylough’s woes as Daly’s goal was tool little to late.
An Cheathrú Rua cruised to victory over Barna, winning on a scoreline of 0-13 to 0-7. Barna failed to score from play as Sean McGabhain, Cillian and Ciaran de Paor were on song for An Cheathrú Rua.
Tuam Stars coasted to a 1-13 to 1-2 victory over neighbours Cortoon Shamrocks after a comprehensive opening half set them up for victory. The Stars led by 0-8 to 0-2 at half time and simply added to the scoreboard in the second half. Cortoon’s only score in the second half was a goal from a penalty by Derek Savage, but Conor O’Doherty’s late strike ended Cortoon’s challenge.
Kilkerrin/Clonberne edged out Annaghown by 2-16 to 1-17 after extra-time after the sides had drawn 1-13 apiece in normal time.