American second seed Stephens, 22, battled to a 6-4 4-6 7-6 (7-5) victory over Cibulkova in three hours, five minutes on Saturday.
The tie-break was a topsy-turvy affair but Stephens managed to hold her nerve, closing out the match at the third time of asking to add the Acapulco crown to this year's ASB Classic trophy and the 2015 Citi Open.
Stephens stormed out of the blocks, breaking in the opening game before consolidating in the second, and she almost opened up a commanding 3-0 lead, but Cibulkova fended off two break points to get on the board.
The pair exchanged breaks until Stephens broke in the seventh game and she went on to hold for a 5-3 advantage, a lead she never relinquished in the first set.
Stephens continued where she left off in the second set, threatening to run away with the title after taking a 3-1 lead.
But Cibulkova refused to surrender, reeling off three consecutive games to hit the front, and she did not look back, forcing a deciding set.
The final set - on serve until the fifth game - was a see-sawing battle, with both players earning opportunities to assert their dominance without success.
Some heavy hitting saw Stephens hold serve at 4-4 following a marathon 20-point game.
Stephens then thought she had claimed the decisive break in the 11th game at 30-40 but Cibulkova's challenge showed her forehand caught the line.
And after fending off another break point, Cibulkova went on to win the next three points with some impressive corner-to-corner hitting as a tie-break loomed.
At 2-2 in the tie-break, Cibulkova had the chance to move clear but she was unable to put her volley away and the Slovak then sent a forehand into the net to hand Stephens the trophy.