With their running ambitions frustrated, England pressed for a score through the pack.
A prolonged spell in the vicinity of the Samoan line was eventually broken as the biggest of a succession of Samoan hits, from Seilala Mapusua on Mark Cueto, turned over possession.
Samoa had no such problems as they crossed for their first try at Twickenham in the first minute of the second half.
England's defence never managed to reorganise after seeing the ball pinched from Hape and, after a swift recycle, Williams glided over in the left corner.
Uncertainty seemed to fill Twickenham and Mapusua's audacious, but off-target, drop-goal attempt briefly threatened to extend the lead and further spoil the mood.
The tension was eased as Banahan dived in under the posts after Bath colleague Hape had fixed the short-side defence with a dummy scissors and Ashton drew the final defender.
Matt Banahan crosses for England's first try
The Samoan defence was regularly stretched and it took a superb last-ditch tackle from George Pisi to force Cueto into touch as he shipped inside.
The Islanders were eventually broken however as Banahan stretched to snaffle a wayward pass and Danny Care scampered upfield to set up fellow substitute Croft.
Croft seemed to have denied the Samoans a second try at the other end as he dislodged the ball from George Stowers' grasp inches above the line, but, in the last play of normal time, Otto held on to a loose ball out wide to convert an overlap into a well-deserved score.
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