But there was nothing the American keeper could do to prevent Jarvis from equalising with his cross on the hour mark.
BBC: Emile Heskey celebrates scoring his late winner at Wolves
But the Blues responded with two quick strikes in as many minutes with Kingsberry turning in a Mark Picking cross and Thompson grabbing his hat-trick with a simple tap-in on 75 minutes.
Ryan McIlmoyle drew O'Hare out of the Coleraine goal after collecting Mark McCann's cross from the right but his goal-bound strike was blocked by team-mate Timmy Adamson.
Hull started strongly and Brown, along with most of the home fans, felt they should have had a penalty when Nicky Barmby met Stephen Hunt's lobbed cross and saw his shot come off Maynor Figueroa, only for referee Mark Clattenburg to wave away their claims of handball.
Coached by Argentine Marcelo Bielsa, they could have taken a 10th-minute lead after a brilliant move saw Jean Beausejour - a winger who plays for Club America in the Mexico - execute a clever one-two with Jorge Valdivia, but Mark Gonzalez failed to connect properly with his low cross.
Whittingham was no more than three yards out when he put Mark Kennedy's driven low cross wide, and then McCormack scuffed his shot wide after running clear of the home defence.
With time running out, Mark Hands found himself free down the right-hand side and his cross was met by Byrne, whose finish finally banished all Redditch fears of relegation.
Brian O'Driscoll soon made his mark though and cut through the Ospreys back-line before releasing Kearney to cross for his side's second-try.
The court ruled that Judge Lance Ito must vacate his order which tells the jury that former LAPD Detective Mark Fuhrman was unavailable for cross-examination.
When Kevin Doyle held off Brede Hangeland on the right there looked to be little real danger, but the Irishman clipped an enticing cross to the back post and Van Damme side-footed the ball back across a scrambling Mark Schwarzer to claim his first goal for the club.
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