It was a largely frustrating night for the visitors, who were forced to wait until the 53rd minute to break the deadlock against the minnows when Harry Kane scored his first goal of the season.
It looked as though that would be the deciding goal too, but Ryan Bertrand opened his England account with four minutes remaining before Danny Welbeck and Kane embroidered the win with stoppage-time strikes.
The result means that England remain top of Group F, two points clear of second-placed Slovakia ahead of Monday's meeting between the two sides at Wembley.
Manager Gareth Southgate, whose first match in charge of the team came in the reverse fixture last October, handed the captain's armband to Jordan Henderson following Wayne Rooney's retirement, while Joe Hart retained his place in goal for the visitors.
It was his opposite number Andrew Hogg who was the busier of the two keepers in the opening exchanges, though, thwarting Raheem Sterling inside the first minute after the Manchester City man had delayed his shot when through on goal.
Malta's only goal in their four previous meetings with England was an own goal from Richard Wright in 2000, but they almost doubled that tally in spectacular fashion when Ryan Fenech's speculative 30-yard volley drifted narrowly over the crossbar.
England then created another clear chance of their own in a lively start to the game, but Kane saw his powerful downward header turned away by a smart save from Hogg as the Tottenham Hotspur striker's wait for a first goal of the season went on.
Despite their bright start, the chances soon dried up for the visitors and the rest of the half was a tale of frustration, with Dele Alli blazing one sight of goal well over the crossbar.
England did have the ball in the back of the net midway through the half when Phil Jones nodded Henderson's corner past Hogg, but the referee was quick to disallow the goal for a foul on the goalkeeper.
A tame shot from Alex Oxlade-Chamberlain - fresh from his deadline day move to Liverpool - in stoppage time was the only other work Hogg had to do before half time, and the whistle was greeted with boos from the visiting fans as England went into the break goalless against a team ranked 190th in the world.
Malta almost inflicted more misery on England with the first sight of goal in the second half as captain Andre Schembri flashed an effort narrowly past the post from outside the area.
England did finally break the deadlock in the 53rd minute, though, and it was Kane who opened his account for the season when he swept the ball home from close range after good work by Tottenham teammate Alli.
It was Kane's fourth goal in his last three England games, and came following another goalless August for Spurs in the Premier League.
Malta continued to create the odd sight of goal themselves, with Ebbsfleet United full-back Sam Magri firing one well wide shortly before the hour mark as England failed to build on their opening goal.
Hogg was tested a couple of times, but it was only from long range as both Kane and Marcus Rashford drew saves from the Malta keeper with good efforts from outside the area.
It was a long-range strike which handed England their second goal as Bertrand tried his luck from range, and this time Hogg was unable to get down in time to prevent the Southampton full-back scoring for his country for the first time.
A third goal soon followed as the clock ticked into three minutes of injury time, with Welbeck marking his first England appearance for 18 months by getting on the end of Kane's cross and lifting the ball past Hogg, who had come off his line.
The mostly uninspiring and unconvincing performance was then treated with a flattering fourth just a minute later as Kane doubled his tally for the evening, applying the finishing touch to Rashford's defence-splitting pass - although Malta's players were unhappy that the Manchester United man didn't kick the ball out while they had a player down.
Aside from giving the scoreline a more one-sided look the goal had little bearing on the result, though, and the final whistle blew moments later as England picked up their first away victory under Southgate.
The Three Lions are now unbeaten in their last 18 World Cup qualifiers, while Malta have lost their last 11 and remain without a single point in the current campaign.