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Joseph, who was only called up to the starting XV on the morning of the match after Sailosi Tagicakibau failed a fitness test, scored his third Exiles try with just four minutes to go and looked to have snatched a remarkable victory only for Nick Abendanon to score the decisive try in the dying minutes.
With the two sides being bonus point winners in week one of the new Aviva Premiership season, many pundits were predicting a feast of tries and attacking rugby in fine weather conditions.
What the crowd of just over 11,000 got instead was a compelling, tight contest that went down to the wire.
The Exiles were forced to make two late changes to their line up after Tagicakibau and David Paice failed fitness tests on the morning of the match with Joseph and James Buckland coming into the line-up and Tom Homer, Darren Allinson and Rob Herring being called up to a re-jigged bench.
Irish were on the score sheet as early as the third minute after Ryan Lamb got things underway with a well struck penalty after Simon Taylor was penalised at the breakdown.
That lead was short lived, however, as Olly Barkley hit back with three points of his own less than two minutes later.
The early action was played at a lung busting pace, so much so that Bath fullback Nick Abendanon was forced to play without his right boot during five successive minutes of play after losing it in a ruck.
For all the wealth of skilful and creative players on the pitch, it was defence that dominated the opening quarter, and indeed the match, as both sides put on a defensive masterclass.
The ferocity of the contest claimed four victims in the first half as Lee Mears, Matt Banahan and Simon Taylor for Bath and Irish’s influential flanker Steffon Armitage all had to leave the pitch due to injury.
With the half hour mark approaching, Barkley gave his side the lead for the first time before completing a first half hat-trick of penalties two minutes from the whistle.
Not to be outdone, Lamb reduced the deficit with a second penalty of his own with the last kick of the half to leave Bath with a narrow 9-6 lead at the break.
The hosts tried to raise the tempo of the match after the restart but again defence led attack until Elvis Seveali’i was sent to the sin bin by referee Andrew Pearson for an adjudged dangerous tackle.
Barkley soon compounded the situation by kicking his fourth penalty of the afternoon and the England centre brought the home support to their feet moments later when he charged through a gap and surged upfield. The Exiles defence scrambled back and Paul Hodgson reacted the quickest to clear the danger.
As they had done the previous week at Twickenham, Irish kept parity with their opponents when a man down, but just as Seveali’i was preparing to return to the action, Stowers was dismissed for a challenge on Nick Abendanon.
The odds were now firmly stacked against the visitors, but Toby Booth’s London Irish squad is resilient to the very core and they came back into the match in the most dramatic style with Joseph’s try.
It all started with a searing break from the teenage wing who slalomed his way through the Bath ranks before being bought down near the 22.
From the resulting position, Irish moved purposely upfield with substitute Seilala Mapusua doubling up as a number eight in a series of powerful drives.
With the tryline just inches away, the Exiles opted for width and Lamb fizzed a perfect pass out to the left flank where it found the hands of Joseph to score his first Premiership try.
Lamb then converted from right on the touchline and the Exiles had the lead.
The delirium was sadly short lived as Abendanon finished a slick Bath move to regain the lead and Barkley confirmed the win with a penalty right at the death.
Bath: Tries: Abendanon (74). Penalty goals: Barkley (5, 28, 38, 54, 80).
London Irish: Tries: Joseph (72); Conversion: Lamb (73). Penalty goals: Lamb (3, 40).
Scoring sequence(London Irish first): 3-0, 3-3, 3-6, 3-9, 6-9. HT. 6-12, 13-12, 13-17, 13-20.
London Irish: 15. Delon Armitage; 14. Topsy Ojo; 13. Elvis Seveali’i; 12. Daniel Bowden (Mapusua 62); 11. Jonathon Joseph; 10. Ryan Lamb; 9. Paul Hodgson (Allinson 69); 1. Clarke Dermody (captain) (Lahiff 62); 2. James Buckland; 3. Faan Rautenbach (Corbisiero 50); 4. Kieran Roche; 5. Bob Casey (Kennedy 58); 6. Declan Danaher; 7. Steffon Armitage (Garvey 22) ; 8. George Stowers.
Replacements not used: 16. Rob Herring; 22. Tom Homer.
Bath: Bath: 15. Nick Abendanon; 14. Matt Carraro, 13. Shontayne Hape, 12. Olly Barkley, 11. Matt Banahan (Biggs 20); 10. Sam Vesty, 9. Michael Claassens; 1. David Flatman (Catt 42), 2. Lee Mears (Dixon 22), 3. David Wilson (Bell 69), 4. Stuart Hooper, 5. Danny Grewcock (Skirving 69), 6. Simon Taylor (Beattie 35), 7. Lewis Moody, 8. Watson (capt).
Replacements not used: 21. Mark McMillan, 23. Jack Cuthbert.