Hull midfielder Robert Snodgrass continued his impressive start to the new season by netting a hat-trick, while new Fulham loan signing Chris Martin and Sheffield Wednesday frontman Steven Fletcher scored in the second half.
Gordon Strachan’s side had been given a scare when Malta equalised on 13 minutes through Alfred Effiong, although the hosts ended proceedings with nine men after both Jonathan Carusana and Luke Gambin were sent off.
The Scot’s last successful qualifying campaign ended with a trip to the 1998 World Cup in France, while victory against Malta propelled them ahead of England to the summit of Group F.
Northern Ireland, meanwhile, who reached the knockout stages of Euro 2016 during the summer, opened their account with a goalless draw against Czech Republic in Prague.
“We are satisfied,” said skipper Jonny Evans. “We didn’t create too much and they had a lot of pressure towards the end, and we battled to keep a clean sheet. It’s not a bad result away from home to take a point.”
World champions Germany sent out an ominous message to their Group C opponents, including Northern Ireland, by thrashing Norway 3-0 in Oslo.
Bayern Munich forward Thomas Muller netted twice, either side of Joshua Kimmich’s maiden international strike.