At lunch on the fourth day England, in their second innings, were eight without loss - a lead of 124 - with captain Andrew Strauss six not out and Alastair Cook unbeaten on one.
Left-arm spinner Panesar's haul of six for 129 in 36.1 overs was the fourth time in his 14 Tests that he has taken five or more wickets in an innings.
Suggestions he be omitted because conditions would not be in his favour had already been made to look foolish by the 25-year-old.
And with England a pace bowler down as Matthew Hoggard remained off the field and in the absence of the already-injured Andrew Flintoff, it was largely down to Panesar that England were able to stay on top in a match that could yet end in a draw.
West Indies resumed on 363 for seven, 190 runs behind England's first innings 553 for five declared but having survived the follow-on with senior batsman Shivnarine Chanderpaul 63 not out.
At that stage Panesar had taken four wickets for 108 runs in 31 overs, 29 of them unchanged, but received little support at the other end with fast bowler Stephen Harmison (none for 95 off 22 overs) disappointingly off-target.
Meanwhile Hoggard remained in the pavilion with the thigh muscle injury that saw him miss most of Saturday's play.
Left-hander Chanderpaul, who'd shared stands of 92 with Dwayne Bravo (56) and 83 with wicket-keeper Denesh Ramdin (60) on Saturday, looked in fine touch when on-driving Harmison's third ball Sunday down the ground for four.
But he became Panesar's fourth lbw victim of the innings when the Northamptonshire bowler, who'd taken a wicket first ball on Saturday, struck with his fourth Sunday when Chanderpaul, on 74, was hit on the back leg by a ball that gripped and turned out of a footmark.
Chanderpaul, who in the Lord's Test three years ago scored 128 not out and 97 not out, had batted for over four hours and faced 193 balls with nine fours.
Daren Powell and Jerome Taylor chanced their arms before Taylor, on 21, was caught at cover-point by substitute fielder Lee Hodgson off Harmison.
The England quick had had to wait until his 27th over for a wicket in his first international match since the Ashes tour.
But Powell then gave himself room outside leg-stump to belt Harmison through mid-off for four in flamboyant style and next ball followed that up with a textbook cover-driven boundary.
Panesar restored order when last man Corey Collymore become his fifth lbw victim of an innings where the tourists struggled with his arm-ball.
Powell was 36 not out off 60 balls with seven fours, West Indies 116 behind.
Harmison, who missed the World Cup after retiring from one-day internationals, finished with one for 117 from 28 overs.
Together with fellow Durham quick Liam Plunkett he conceded 16 wides in a high extras total of 40.
England's innings featured four hundreds with Matt Prior's unbeaten 126 the first by an England wicket-keeper on Test debut.
Collingwood (111), Ian Bell (109 not out) and Cook (105) also reached three figures as four England batsmen scored centuries in the same Test innings for the first time in 69 years.
England first innings: 553/5 declared Vs West Indies first innings: 437 all out ( Gayle 30, Ganga 49, Smith 21, Sarwan 35, Chanderpaul 74, Bravo 56, Ramdin 60, Powell 36, Taylor 21)