Southgate's first game in charge since taking over from the sacked Sam Allardyce saw England enjoy a fluent first half and the vast majority of possession before tailing off in the second half.
As announced 24 hours before the match, Theo Walcott was rewarded for his good form with Arsenal with a starting spot while Wayne Rooney continued as captain, in a deeper midfield role and Jesse Lingard was given his debut on the wing.
An early injury to Ryan Bertrand saw a change at full back as Danny Rose came on after 19 minutes but England took the lead 10 minutes later.
Jordan Henderson, who enjoyed one of his best games in an England shirt in midfield, delivered the cross and his Liverpool team-mate Sturridge headed the ball back into the corner.
Captain Rooney fired an early shot over and later tested the goalkeeper with a fine free kick, but was also lucky to still be on the pitch after a nasty- looking challenge on Andre Schembri.
But it needed Alli to settle things down with the second goal, following up after his first attempt was well saved.
England continued to dominate in the second half and Walcott forced another decent save from the visitors' goalkeeper, Andrew Hogg.
That was almost Walcott's last input as Marcus Rashford replaced him with just over 20 minutes and Jamie Vardy came on for Sturridge as the hosts pushed for a third goal.
Joe Hart had little to do in the England goal but reacted well when he turned Andre Agius's volley around the post late on, Malta's only shot on goal all night.
Dele Alli might have made it 3-0 with the clock ticking down but his volley went over and England had to settle for a two-goal margin, prompting a few boos from the 80,000-plus crowd.
Henderson said Alli was perfectly suited to the No 10 role, just behind the striker.
"Me and Wayne Rooney need to get the ball forward and offer protection when we lose the ball," Henderson said.
