Strauss will return to the crease on 121 after placing England in charge of the first Investec Test against the West Indies.
A square cut off Darren Sammy, the West Indies captain, gave Strauss his first top-level century since his second-innings 110 in the Ashes-opening draw in November 2010.
"It's been a while, so it's one of the more special [hundreds]," he said. "It's been a long wait, but it makes it all the more special.
"As the pressure builds, you really want to release it, you're wanting to take that monkey off your back and wanting to contribute to the team, and I was able to do that. It feels really good tonight and I might have a little glass of something."
Reflecting on the decisive shot, he added: "I was just waiting for the cut ball. He [Sammy] hadn't bowled one for about 10 overs, but, thankfully, it came.
"It was a very special ovation, it did go on and on. It was slightly emotional and I had to take a couple of moments. It's not that often in your career you get to score a Test century and you have to enjoy them."
Strauss' long, barren run had caused pressure to build on his place as captain and at the top of the order, but the reaction of his team-mates – notably the bear-hug he received from Kevin Pietersen, his batting partner – demonstrated the regard in which he is held.
"When one guy's under the pump a little, we always want to see him do well," added Strauss. "We've seen it happen to numerous of our players, including myself in the past; it becomes the talking point. Hopefully, it will move on to someone else now."
Strauss moves alongside Pietersen at fourth on the all-time list of England centurions.
After the loss of his opening partner Alastair Cook, who edged on to his stumps after a risk-filled 26, Strauss shared a stand of 147 with Jonathan Trott (58) on a benign pitch but under cloudy, floodlit skies.
Sammy should have had Trott caught-behind on the same score, but a half-hearted appeal led to a decision to resist DRS. Trott survived to complete his 105-ball 50 just before tea, only to fall in early evening when he went to drive Sammy on the up and edged to Denesh Ramdin behind the stumps.
Pietersen then ushered Strauss past his hundred, and dominated a partnership of exactly 50, before edging a cut at Marlon Samuels into Ramdin's gloves. Strauss resumes this morning with Ian Bell for company.
Earlier, Stuart Broad, who finished the first day by taking the wicket of Fidel Edwards, needed just one ball yesterday morning to consign Shannon Gabriel, the debutant No.11, to a golden duck. Broad sent one down on a length around off-stump and Graeme Swann took the edge at second slip to close the tourists' first innings and give Broad career-best figures of seven for 72.
Shivnarine Chanderpaul, therefore, was left unbeaten on 87, in a total which Strauss and England would prove significantly under-par.