Salpingidis netted after 58 minutes to reward a Greek performance which was dominant in terms of attacking possession, even if clear-cut chances were at a premium.
The win, which had shades of their previous laborious victory over Liechtenstein about it, meant Greece stayed level with Bosnia-Herzegovina, who beat Slovakia 2-1, at the top of the World Cup qualification group, while also assuring them of second place at the very least.
The game took an unsavoury twist at the end, as Latvia defender Ritvars Rugins was sent off for violent conduct in the 86th minute before Greece midfielder Kostas Katsouranis was also shown a red card in the 90th minute for his second bookable offence.
Greece made a lively start and could have been 2-0 up inside 10 minutes.
First Kostas Mitroglou sent a header in on goal in the fifth minute but Latvia goalkeeper Aleksandrs Kolinko held on.
Then four minutes later Salpingidis had a chance from close range but he could not find the target with his left-foot effort.
Mitroglou had another chance just after the half-hour mark but this time his header was wide.
Again it was Greece doing most of the running at the start of the second half and they were rewarded with a goal just before the hour mark.
Georgios Samaras played in Salpingidis, who sent a left-foot strike low past Aleksandrs Kolinko from close range.
Chances were few and far between from there on with Greece content to protect their lead.
They came away with the win they needed, though their inferior goal difference means they remain second favourites to win the group.