When bad light ended play, England were 259 for three -- a lead of 16 runs after they needed just Friday's first ball to dismiss the West Indies for their overnight score of 243.
Strauss was 121 not out and Ian Bell five not out at stumps.
But with the West Indies just two deliveries into the new ball, England's position is far from assured in this first of a three-Test series.
This was the 35-year-old Strauss's 20th century in his 95 Tests but the left-handed opener's first since he made 110 against Australia at Brisbane in November 2010.
He came into this match with questions regarding his recent lack of runs but the circumstances were near ideal for Strauss to end his century drought, despite overcast conditions that saw the floodlights switched on after lunch.
The West Indies attack was willing but rarely threatening and Strauss enjoys batting at Lord's, his Middlesex home ground, where he has now made five Test centuries including one on debut, against New Zealand in 2004.
Strauss is now in sight of the England Test record of 22 hundreds held jointly by Walter Hammond, Colin Cowdrey and Geoffrey Boycott.
His only worrying moment Friday came when he was dropped on 95 in the slips by Shivnarine Chanderpaul off what was, in any event, a Fidel Edwards no-ball.
Soon afterwards Strauss, playing his favoured cut shot, struck West Indies captain Darren Sammy for the 17th four of a 213-ball hundred and punched the air in celebration.
But West Indies enjoyed a welcome moment of respite when Kevin Pietersen, who'd looked in excellent touch while making 32 and putting on exactly 50 with Strauss, saw an edged cut off occasional off-spinner Marlon Samuels well caught by wicket-keeper Denesh Ramdin.
It was a much needed break for the tourists who, after Kemar Roach had made Strauss's fellow opener Alastair Cook play on for 26, had to endure a second-wicket stand of 147 featuring Jonathan Trott's 58.
Sammy, who twice came close to having Trott out for 17 after lbw and caught behind appeals were rejected, eventually got his man when Ramdin held an outside edge from the right-hander.
Earlier, West Indies saw No 11 Shannon Gabriel's maiden Test innings end in a golden duck when he edged Stuart Broad to Graeme Swann at second slip.
Chanderpaul remained stranded on his overnight score of 87 not. The left-hander, officially the world's best Test batsman, was in for more than four hours and struck 12 boundaries.
Fast-medium bowler Broad's figures of seven for 72 were his best in Tests, surpassing his six for 46 against India at his Nottinghamshire home ground of Trent Bridge last year.
During the course of this return, Broad, son of former England opening batsman Chris, became only the seventh player in history to take both five or more wickets in a Test innings and score a Test century at Lord's following his 169 against Pakistan at 'the home of cricket' two years ago
