England, showing eight changes from the team that started Friday's 2-0 win over Estonia at Wembley, put themselves into a commanding position after scoring two goals which went in off the same right-hand post inside the opening 35 minutes.
The first, after 29 minutes, was a powerful long-range strike from Ross Barkley that took a deflection off a defender before flying into the net.
Six minutes later another well-struck shot from Harry Kane hit the post and struck the back of keeper Giedrius Arlauskis who conceded an own goal as the ball rebounded into the net.
Alex Oxlade-Chamberlain blasted England's third at Arlauskis's near post after 62 minutes as they became the only team in this qualifying competition to win all their matches.
England coach Roy Hodgson said he was proud of his squad's achievement, but was not getting carried away with far tougher opposition to come in next year's finals.
"Of course to get 10 wins out of 10 in these qualifying groups is never easy so we have to satisfied with it and be proud, it was a nice way to end what has been an excellent qualifying campaign for us," Hodgson told ITV Sport.
England have tough friendlies organised against European champions Spain, Euro hosts France and world champions Germany before the finals.
"We know by going to France we will come across much better opposition, teams that are more capable of causing us problems and we will see how we will deal with that," Hodgson said.
England sealed their place at Euro 2016 last month and never remotely looked like squandering the chance of joining France (1992 and 2004 qualifying), Czech Republic (2000), Germany and Spain (both 2012) as the only countries to achieve a perfect qualifying record.
The victory, on a chilly night and on an artificial surface in the Lithuanian capital, meant England finished the campaign with 30 points, followed by Switzerland 21, Slovenia 16, Estonia 10, Lithuania 10 and San Marino one.
(Writing by Mike Collet in London; editing by Martyn Herman and Ed Osmond)
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