Trailing the pacesetters by four points after Greece edged Israel 1-0 earlier in the day, Croatia had no margin for error against a home team who had lost their opening six games.
Defender Dejan Lovren wrapped up the points for Slaven Bilic's side with a third goal midway through the second half after Malta had briefly revived their hopes thanks to captain Michael Mifsud late in the first half.
Croatia took only 11 minutes to open the scoring. Receiving a pass just outside the penalty box, Ognjen Vukojevic hit a firm drive that took a deflection as it sailed past goalkeeper Andrew Hogg.
Malta came close to equalising midway through the first half when John Hutchinson's effort from outside the box flew just wide of Stipe Pletikosa's left-hand post.
After Darijo Srna threatened a second goal with a swerving free-kick, Croatia eventually extended their lead on 32 minutes. Sime Vrsaljko flicked the ball towards Milan Badelj who ran through to beat Hogg from close-range.
Malta grabbed a lifeline seven minutes before half-time when Mifsud netted after good work by Roderick Briffa.
Croatia sealed their win on 68 minutes when Lovren beat Hogg with a downward header after a good cross by Badelj from the right.
