Spain maintained their six-point lead at the top of Group I after Valencia CF's Juan Mata helped force a Lithuania own goal before scoring himself to deny Raimondas Žutautas's men a point.
Xavi Hernández made the breakthrough for the visitors, his deflected effort looping over Žydrūnas Karčemarskas after 19 minutes, but a brilliant volley from Marius Stankevičius drew the Baltic nation level just before the hour. Mata, however, proved to be Spain's trump card. First, Tadas Kijanskas inadvertently directed his cross past Karčemarskas, before the 22-year-old was set up by fellow substitute David Silva to score his side's third.
Having drawn 0-0 in Lithuania seven years ago, Spain did not dazzle at first, but after Deividas Šemberas intervened to give Xavi a somewhat fortuitous opener, Karčemarskas was forced to deny Fernando Llorente a second when he went through on goal. The best Lithuania could offer in return in the opening period was a raking Mindaugas Panka effort, saved by Iker Casillas.
The visitors looked strong from the restart, with the lively Llorente testing Karčemarskas again following a mazy dribble, but they were hit with an improbable blow as Valencia defender Stankevičius volleyed a Spanish clearance straight back into Casillas's net from 25 metres.
Karčemarskas was then called on to fend away a Xabi Alonso free-kick, but he could do nothing to prevent Kijanskas unfortunately restoring Spain's lead. While Tomas Danilevičius had another go from distance, the visitors had the final word, with Mata finishing from close in after Silva's first-time ball showed him a sight of goal.