Paulino's two-run homer highlighted a three-run seventh in which Cody Ross stole home, giving the Marlins a 4-2 lead and sending the Cubs to their sixth loss in seven games.
Robertson (3-3) allowed two runs and seven hits after dropping his previous three starts.
Chicago's Ted Lilly (1-3) took a no-hitter into the sixth before things unraveled. Alfonso Soriano had three hits, including two run-scoring singles, and threw out Hanley Ramirez trying to score from second on Jorge Cantu's single to left in the eighth.
But it was a miserable night for rookie phenom Starlin Castro.
After setting a major league record by driving in six runs in his debut at Cincinnati on Friday, he struggled in his first appearance at Wrigley Field. The shortstop committed three errors, giving him four in as many games, and went from hearing loud cheers to loud boos.
Fans really let him have it in the eighth, when he let Ramirez's grounder go under his glove as he tried to backhand it and then took his time retrieving the ball in shallow left. Soriano kept it a two-run game with a strong throw home moments later, but the Cubs couldn't pull this one out.
Lilly was a tough-luck loser, dropping his third straight start even though he only allowed five hits in seven innings.
The Marlins did not get a hit until Chris Coghlan's RBI double with one out in the sixth, which came after Castro overthrew first on Brett Carroll's leadoff grounder, to tie it at 1.
The Cubs took the lead in the bottom half when Aramis Ramirez's wind-blown pop drifted toward the middle of the infield and eluded first baseman Gaby Sanchez, dropping in for a single. After a wild pitch, he scored from second on Soriano's single to left, but Lilly couldn't hold the lead.
He gave up a single to Dan Uggla with one out in the eighth before Paulino drove a slider off the basket in left field for his second homer, pointing toward the sky as he rounded first. The Marlins got another run on a double steal, when Lilly tried to pick off Cameron Maybin at first and Cody Ross raced home to make it 4-2.
Leo Nunez worked the ninth for his sixth save in eight chances.
NOTES: The Marlins activated LHP Dan Meyer, who had been on the 15-day disabled list since April 26 because of a strained left calf. ... Soriano has a nine-game hitting streak. ... Cubs manager Lou Piniella said LHP John Grabow was "ready to go" after getting a cortisone shot for his sore left knee. ... The Cubs will give their starters an extra day of rest rather than juggle their rotation with an off day Thursday. ... There was a moment of silence before the game for Hall of Fame pitcher Robin Roberts and broadcaster Ernie Harwell, who both died last week. ... Butler coach Brad Stevens threw out the first pitch and led the seventh-inning rendition of "Take Me Out to the Ballgame."