Edinburgh’s second victory on the road — and second ever in France —keeps the heat on Cardiff Blues as they hunt for their first quarter-final spot in eight years.
Back row trio Ross Rennie, Netani Talei and David Denton all crossed as the visitors led for the majority of the game.
But Racing responded with three tries of their own and looked set to share the spoils before Godman struck.
Scorers for Racing Metro 92: Tries: Steyn, Jose Imhoff, Battut. Cons: Hernandez 2, Descons. Pen: Wisniewski.
Scorers for Edinburgh: Tries: Rennie, Talei, Denton. Cons: Laidlaw 3. Pen: Laidlaw. Drop Goal: Godman.
RACING METRO 92: Jose Imhoff, Vakatawa, Steyn, Estebanez, Saubade, Hernandez, Descons, Lo Cicero, Orlandi, Nallet, Van der Merwe, Leo’o, Battut, Chabal, Arganese.
Replacements: Vaquiin for Vakatawa (74), Wisniewski for Hernandez (57), Loree for Descons (71), Sa for Orlandi (50), Le Roux for Chabal (65), Bianchin for Arganese (65).
EDINBURGH: Paterson, Jones, De Luca, Scott, Visser, Laidlaw, M Blair, Jacobsen, Ford, Cross, Gilchrist, Cox, Denton, Rennie, Talei.
Replacements: T Brown for Paterson (70), Godman for M Blair (67), Gilding for Cross (67), Grant for Rennie (49).
THE Ospreys kept alive their hopes of reaching the quarter-finals of the Heineken Cup with a six-try romp against Treviso.
The hosts had secured the bonus point after just sixminutes of the second half as a penalty try added to Ashley Beck’s first-half brace and Tommy Bowe’s interception score, with replacement Kahn Fotuali’i and a second penalty try completing the scoring as fly-half Dan Biggar kicked 12 points.
Edoardo Gori and Gonzalo Padro crossed for the visitors but Ospreys now need a bonus point win in Biarritz and hope other results go their way to progress.
Scorers for Ospreys: Tries: Bowe, Beck 2, Penalty 2, Fotuali’i. Cons: Biggar 3, Morgan. Pens: Biggar 2.
Scorers for Benetton Treviso: Tries: Gori, Padro. Cons: Burton, Botes. Pen: Burton.
OSPREYS: B Davies, Bowe, Bishop, Beck, Williams, Biggar, Webb, James, Hibbard, A Jones, Gough, Evans, Smith, Tipuric, Bearman.
Replacements: Isaacs for Bowe (72), Morgan for Biggar (61), Fotuali’i for Webb (61), Bevington for James (46), Bennett for Hibbard (47), Jarvis for A Jones (55), O’Toole for Gough (70), J Thomas for Bearman (52).
BENETTON TREVISO: Williams, Nitoglia, Sgarbi, Pratichetti, Iannone, Burton, Gori, Rizzo, Sbaraglini, Cittadini, Padro, Bernabo, Derbyshire, Zanni, Filippucci.
Replacements: Semenzato for Pratichetti (53), Botes for Burton (44), Van Zyl for Gori (77), Allori for Rizzo (44), Rouyet for Cittadini (44), Vermaak for Derbyshire (16), Picone for Filippucci (64).
Referee: JP Doyle (RFU).