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Despite being depleted by injuries which cost them the services of James Scaysbrook, Peter Dixon and Aaron Jarvis inside the opening 48 minutes, the Bath pack finally out-muscled their Irish counterparts.
They were trailing 17-10 when they won a lineout near the Irish line, enabling them to power flanker Jonny Fa'amatuainu over in the right-hand corner, with Shaun Berne converting to put them level at 17-17.
Irish regained the lead, which they had held for most of the match when debutant fly-half Eoghan Hickey landed his fifth penalty from five attempts.
But Grewcock, left out of England's World Cup squad following suspension which would have meant him missing their opening three matches, had the final say.
It was tough on Hickey, the 24-year-old fly half signed from Munster during the summer.
Called up because of injuries to Shane Geraghty and Jeremy Staunton, he marked his first Guinness Premiership appearance with an impeccable goal-kicking display.
The newcomer was also instrumental in the build up to the opening try, scored by the home side after half an hour.
His probing kick was knocked into touch by Bath full-back Michael Stephenson. Irish won the resulting lineout and drove hooker David Paice over the line.
Bath, who had been forced to defend stoutly as Irish made a promising start, squandered a great opportunity for a try when Ian Davey's hurried pass was dropped by centre Berne, whose unhappy first half also included missing two penalties from comfortable kicking range.
Davey made amends after 35 minutes, taking a pass from Fa'amatuainu and showing an electric burst of acceleration to slice through the Irish defence and touch down between the posts, leaving Berne an easy conversion which he managed this time.
Berne was on target again with a close range penalty three minutes into the second half to cut the deficit to one point.
But Hickey, who had landed two first half penalties, struck two more - one a superb effort from near the touchline 45 metres out, to put Irish seemingly back in control at 17-10 ahead.
Bath, who made their fourth forward change when David Barnes replaced former England prop David Flatman, turned on the power up front to finally overwhelm the home side, who lost for the third time in four league matches this season.
London Irish (11) 20
Tries: Paice
Pens: Hickey (5)
Bath (7) 22
Tries: Davey, Browne, Grewcock
Pens: Berne
Cons: Berne, Brown
London Irish: Armitage, Ojo, Mapusua, Mordt, Tagicakibau, Hickey, Hodgson; Lea'aetoa, Paice, Rautenbach, Kennedy, Casey (capt), Danaher, Armitage, Thorpe.
Replacements: Warren, Mackie, Murphy, Hudson, Roche, Fury, Ireland.
Bath: Stephenson, Higgins, Cheeseman, Berne, Davey, Davis, Walshe; Flatman, Dixon, Jarvis, Short, Grewcock, Faamatuainu, Scaysbrook, Feaunati.
Replacements: Hawkins, Barnes, Ion, Browne, Lipman, Claassens, Abendanon.
