Shane Williams scored a hat-trick to help the Ospreys to the brink of qualification for the EDF Energy Cup semi-finals.
The Welsh region only require a bonus point in their final Group C match at Harlequins on December 2 to book their place in the last four for the second year running.
In all the Ospreys scored seven tries, six of those unanswered as they came back from 16-13 down after 29 minutes.
In the first eight minutes James Hook and Eoghan Hickey swapped penalties in an error-strew opening.
And the errors continued to come when Ospreys centre Andrew Bishop had his long pass picked off by Tomas de Vedia, who ran in from halfway for a converted try.
But the home side were back on terms at 10-10 when a long Lee Byrne pass put Gavin Henson into space and he put Jonathan Thomas free down the right for the try.
Two more swapped penalties from Hook and Hickey, who also missed two long-range efforts, made it 13-13 on 26 minutes.
The Ospreys continued to give penalties away in their own half and an indiscretion at a line-out led to Hickey planting a third penalty as the Exiles led for a third time at 16-13.
But a neat offload in the tackle from skipper Filo Tiatia sent Williams away for the Ospreys second converted try to give the home side a 20-16 lead after 32 minutes.
In the second half it was one-way traffic as the Ospreys scored five tries to nil.
Mike Phillips started the sequence of scoring before Ben Lewis went over in the corner to claim the bonus point, a scored converted by Hook, who provided 14 points with the boot.
Lock Alun-Wyn Jones went over via a cross-kick and he was followed over twice by Williams to complete a rousing win for the Welshmen.