The sides were level at the interval but Hearts racked up four second-half goals to stay top of the Scottish Championship and leave the Miners with just one point from six games.
Calum Gallagher drew Cowdenbeath level following Billy King’s opener but second-half goals from Jamie Walker, Osman Sow from the penalty spot and two from Carrick gave the Jambos a comfortable win.
Billy King opened the scoring with his third league goal of the season on 15 minutes when he latched onto Danny Wilson’s superb cross and fired past Robbie Thomson.
King almost doubled his tally on 20 minutes when he combined with James Keatings to work an opening eight yards out, but Dean Brett slid in to make a goal-saving tackle.
Cowdenbeath drew level on 24 minutes when he followed up to lash home after Neil Alexander made an excellent save to deny Kudas Oyenuga, who had drifted in behind the home defence.
Heart restored their lead soon after the interval when Walker, from a tight angle at the near post, glanced home a looping header from an Adam Eckersley cross.
Sow made it three from the penalty spot on 55 minutes after Walker was adjudged to have been fouled by Darren Brownlie.
Carrick capped off the scoring ten minutes from time when he spun and drilled home a powerful low shot from the edge of the box.