Captain Gorkss and Verpakovskis struck late in each half to draw the sting out of a battling Malta side keen to atone for their 3-1 defeat away to Israel in their opener last Thursday.
Latvia, who were thrashed 3-0 at home by Croatia in their first qualifier of the campaign on Friday, forced the tempo in the initial stages with Juris Laizans bossing the midfield.
Andrew Cohen's quickly-taken free-kick unsettled the Latvia defence as the Malta forward's long ball invited the speedy Michael Mifsud to run forward.
Malta's growing optimism suffered a blow when Latvia took the lead just over two minutes before half-time. Aleksandrs Cauna's inswinging freekick was met by Gorkss whose header flew past Malta goalkeeper Andrew Hogg.
Malta had a great chance to draw level early in the second half when the dynamic Manny Muscat sped into the box to receive Gareth Sciberras's pass but his curling shot was off target.
Malta were then unfortunate not to equalise with 21 minutes remaining when Cohen guided a pass into the six-yard box after Latvia had only partially cleared Shaun Bajada's corner.
Bogdanovic went close again with a diagonal shot but Malta's hopes of salvaging a point vanished when Latvia increased their lead five minutes from time. Verpakovskis breezed away from Cauna and fired a ferocious drive past Hogg.
