South Africa were 370 for six at stumps, a lead of 23 runs over the West Indies' first innings of 347.
Smith hit a confident 148 to boost his side before Ashwell Prince, who was 41 not out, and Mark Boucher, who was undefeated on 28, put South Africa ahead during their stand of 67.
"It's important that we take a decent lead," Smith told a news conference.
"It's the first time we are putting the West Indies under pressure in the series and a lead of anything over 100 will be very valuable."
Smith's knock took more than seven hours where he faced 313 balls striking 17 fours.
"It's very difficult to score quickly on this wicket," Smith said. "The best time to try and score runs is also the most dangerous time, and that's with the new ball. The West Indies were also very defensive today."
The South African captain was satisfied with his contribution to the team's cause in hot conditions.
"It's great to make runs in tough conditions, and to be able to put the team in a good position," he said.
"It is warm out there, so at times you do lapse. The way to do it is to concentrate ball by ball. You need to work hard, and patience is the key."
The first test of the four match series in Guyana was drawn.
