England enjoyed 71 percent of possession on a slick artificial surface but managed only four shots on target as they failed to penetrate a resolute home defence.
Once again it was captain Kane who made the difference -- taking his goal tally to six in his last seven internationals.
He finished clinically from the spot in the 27th minute after his Tottenham Hotspur team mate Dele Alli tumbled in the area under a clumsy challenge from Ovidijus Verbickas.
There was precious little else to warm the rain-soaked England fans who made the long trip to the tiny stadium.
"It was not a fantastic performance but solid," Kane said. "They didn't create many (chances), we had a few. We were missing a bit of quality really in the final third. The surface was difficult but we have to do better."
England made seven changes from the 1-0 victory over Slovenia on Thursday that guaranteed a sixth successive World Cup qualification -- that match also decided by Kane.
TWO DEBUTS
Two players -- Tottenham's Harry Winks and Leicester City's Harry Maguire -- were handed full international debuts by Southgate while Stoke City's Jack Butland was given a chance to impress in goal ahead of Joe Hart.
Winks had a second-half effort well saved by Lithuania's keeper Ernestas Setkus while substitute Daniel Sturridge's goal-bound shot was blocked late on.
England striker Marcus Rashford occasionally sparked into life but Lithuania generally looked comfortable.
Southgate also experimented with a three-man defence but England looked uneasy at the back against a modest side who have won only one of their last 16 internationals.
Darvydas Sernas went close for the hosts early in the first half and Butland had to make a terrific save to keep out a wayward clearance from England defender Michael Keane.
England are now unbeaten in 21 World Cup qualifiers but the hard work now begins for Southgate who will get a better idea about his side's potential in forthcoming friendlies against world champions Germany and Brazil.
"They had a packed defence, we were a fraction off with our passing," Southgate said, repeating Kane's assertion that England had "lacked quality in the final third."
"It's a completely different challenge against Brazil and Germany next month," added the England manager.
(Reporting by Martyn Herman; Editing by Ken Ferris)
