Smith hit a 133-ball 107 and Pollard belted eight fours and five sixes to frustrate the Irish who won the toss and put the Caribbean side in to bat on an easy-paced track at the Punjab Cricket Association Stadium.
Smith also shared 89 runs with Shivnarine Chanderpaul, opening the innings after Chris Gayle was ruled out on the morning of the match with an abdominal strain.
Kevin O'Brien, who struck World Cup's fastest hundred against England, showed he had the skills with the ball as well, grabbing a career-best 4-71.
A victory for West Indies will virtually assure them of a place in the quarter-finals while Ireland can keep their last-eight hopes alive if they manage to pull off an upset win.
"We wook the batting powerplay early because we had been slow at the start and we wanted to see what would happen," said Pollard.
"I came in during the 32nd over and tried to get runs quickly. I've been backing myself and the team was in a bit of trouble.
"I just wanted to see how long I could bat. Devon Smith batted superbly. My arm is a bit stiff but I'm looking to have a bowl. We didn't get as many runs as we wanted."
Ireland fast bowlers kept things tight in the first 15 overs and did well in the last seven overs, taking the last five West Indies wickets for 53 runs.
The Irish had to wait till the 25th over to pick their first wicket when Chanderpaul (35) chipped O'Brien to short extra cover where captain William Porterfield took a low catch.
O'Brien struck again three balls later in the same over when he uprooted the middle-stump of Darren Bravo before the promising left-hander could even get off the mark.
Left-arm spinner George Dockrell, introduced into the attack late in the 30th over, had Ramnaresh Sarwan caught in the deep for 10 to reduce the West Indies to 130-3.
Ireland were left to rue missed chances against Pollard who was let off twice early in his innings with John Mooney messing up a simple run-out chance and Gary Wilson grassing a catch off Andre Botha.
Pollard punished the Irish, hitting O'Brien for two sixes in four balls to race to his third ODI half-century off 35 balls.
O'Brien returned to take two more wickets, again in the same over, to dismiss Smith and Darren Sammy while John Mooney sent back Pollard and Andre Russell in two balls.