At lunch, West Indies were 212 for four in their second innings.
Left-hander Chanderpaul, officially the world's best batsman, was 73 not out and Samuels 79 not out, with their unbroken fifth-wicket partnership now worth 147 runs.
Even so the West Indies were still just 57 runs in front of England's first innings 398, with the new ball available after just one more over.
But the tourists had at least ensured England would have to bat again if they were to go 1-0 up in this three-match series.
Chanderpaul, one of only 10 batsmen to have scored 10,000 runs in Tests, has now batted for over eight-and-a-half hours in this match having top-scored with 87 not out in the West Indies' first innings 243.
West Indies resumed on 120 for four, 35 runs behind, having lost three wickets with their score on 36 on Saturday.
Chanderpaul was 34 not out and Samuels 26 not out, with their stand then worth 55.
James Anderson and Stuart Broad, who'd taken a Test-best seven for 72 in the first innings, probed for an early breakthrough in overcast conditions but on what was still a typically good Lord's pitch.
Chanderpaul and Samuels almost gifted England a wicket by twice threatening a run out.
But when Broad dropped short, Samuels pulled him past backward short-leg for four. And when the seamer repeated the dose next ball, Samuels commandingly pulled him in front of square for another boundary.
Samuels then off-drove Anderson down the ground for four to complete an admirable 97-ball fifty featuring seven boundaries.
England captain Andrew Strauss switched to the off-spin of Graeme Swann in a bid to break the partnership.
However, Samuels cut Swann's first ball Sunday for a four that took the tourists into the lead and played a near carbon copy next ball.
Chanderpaul had a lucky break when an inside-edge off paceman Tim Bresnan, his sixth boundary of the innings, saw him to a painstaking 151-ball fifty.
But few neutrals would begrudge him a moment of good fortune in yet another marathon effort on behalf of the West Indies.
