England, at lunch on the fourth day, were 202 for six in reply to West Indies first innings 287, a deficit of 85, with fast bowler Edwards's figures now standing at four wickets for 65 runs in 15 overs.
Paul Collingwood, on his Durham home ground, was 35 not out and wicket-keeper Matthew Prior 16 not out.
England resumed on 121 for four, after losing three late wickets on Sunday, with Andrew Strauss 72 not out after the in-form Kevin Pietersen had been caught behind for nought off the final ball of the third day's play.
That left England 166 behind after West Indies, who had been 55 for four, were rescued by Shivnarine Chanderpaul's 136 not out, his second successive hundred, in an innings where left-arm quick Ryan Sidebottom took five for 88, his first five-wicket haul in Test cricket.
Strauss, who had been struggling for the best part of a year, was only able to add five to his overnight when Edwards had the left-handed opener edging a full-length delivery through to wicket-keeper Denesh Ramdin.
His 77, which featured 11 fours, was Strauss's best Test score since his 116 against Pakistan at Headingley in August 2006.
However, England were now 133 for five. Round-arm quick Edwards, after an impressive opening spell Monday of one for 14 in four overs, was replaced by fellow pace bowler Daren Powell.
And Powell had success, two balls after drinks, when Ian Bell was caught by Runako Morton in the gully for 11 after driving loosely at an outswinger.
Now, at 165 for six, England had their last recognised batsman at the crease in Prior, whose first scoring shot was an unconvincing four through the slip cordon off Edwards.
Collingwood was far more authoritative when cover-driving Powell to the boundary and when off-spinner Chris Gayle came on, shortly before lunch, he went down the pitch to loft him over mid-off for another boundary.
West Indies didn't aid their cause by giving away 29 runs in bowling extras, Edwards bowling 10 no-balls alone. England have an unassailable 2-0 lead in the four-match series.
Brief Scores (at lunch, D-4):
West Indies Ist innings 287 (Chanderpaul 136n o; Sidebottom 5 for 88) Vs England Ist innings 202 for 6 (Strauss 77, Collingwood 35 n o, Prior 16 n o; Edwards 4 for 65).