After both sides missed chances in a goalless first half, Natasha Harding headed Wales in front five minutes after the break in Haverfordwest.
Substitute Ward then scored twice in two minutes before sliding in for her third in the closing stages.
Victory sees Wales leapfrog Kazakhstan and Israel into third place in Group 8.
Wales had lost 3-0 away to Austria in their opening fixture before a 4-0 defeat by Norway in October.
The match started in inauspicious fashion as organisers failed to play Kazakhstan's national anthem.
Media playback is not supported on this device
Jayne Ludlow's side started brightly and Nia Jones thought she had headed them in front after nine minutes, only for the goal to be ruled out for offside.
The defender, playing as a striker on this occasion, had a glorious opportunity to score four minutes later but shot wide when clean through in the penalty area.
Kazakhstan had a similarly gilt-edged chance when Wales goalkeeper Alice Evans wandered out of position and Saule Karibayeva's shot was headed off the line by Harding.
The Manchester City forward, switched to left-back for this game, gave Wales the lead five minutes into the second half as she headed in from Sophie Ingle's flick-on.
Wales then took control, as Jess Fishlock set up Ward to fire in after an hour to double the hosts' lead.
The same pair combined a minute later, as Fishlock's through-ball allowed Ward to slot in her second and Wales' third.
Ludlow's side added a final gloss to the scoreline as Ward slid in from Rachel Rowe's pass to complete her hat-trick.
Helen Ward's hat-trick helped Wales women thrash Kazakhstan 4-0 to claim a first win of their Euro 2017 qualifying campaign at the Bridge Meadow Stadium.