Malta threatened an upset after reaching the break on level terms, before Scotland scored four times during the second half as their opponents were reduced to nine men.
It took Scotland just nine minutes to take the lead against the minnows, but their opener was somewhat fortuitous as Snodgrass's attempted cross deceived the goalkeeper and found the top corner of the net.
Midway through the half, Snodgrass should have netted his second when meeting Callum Patterson's delivery, but his header was too close to the goalkeeper.
Despite their status as one of the lowest-ranked nations in world football, Malta were posing a threat to Scotland and they could have taken the lead had Andre Schembri not miscued his header.
The Tartan Army were under pressure to perform after the restart, and although Malta started the second half the brighter of the two teams, Scotland regained the advantage after 53 minutes when Chris Martin converted at the back post after being found by Matt Ritchie.
It got better for the visitors just before the hour when Jonathan Caruana was harshly adjudged to have committed a foul on Martin inside the penalty area and after he was given a red card, Snodgrass stepped up to slot his spot kick into the bottom corner.
Despite all but confirming victory, Scotland still needed goals to improve their goal difference, and they eventually found a fourth when Steven Fletcher rose above the defence to power a header into the corner.
With six minutes remaining, Snodgrass continued his fine start to the 2016-17 campaign by completing his hat-trick when he was on hand to tap into the net from two yards out after Fletcher had struck the woodwork after being sent clear on goal.
Malta were reduced to nine men in added-on time when Luke Gambin directed a kick at Snodgrass but despite the second dismissal, Scotland had to be content with the five as they got up and running with bigger tests to come.