The British No.1 looked in supreme form on Court No.1 against his 26-year-old opponent, recovering from an early break of serve to claim the set in the 12th game.
The Australian Open runner-up enjoyed a run of seven consecutive games in the second set, romping to a 5-0 lead before Hajek finally resurrected his serve to secure his only hold of the set. Hajek did threaten to break Murray in the following game but the Scot fought back to seal the set.
MurrayÃ¢â‚¬â„¢s dominance continued into the third with Hajek offering little resistance. A momentary lapse in the third game of the match aside, Murray’s serve was consistent throughout.
With Hajek unable to make inroads when receiving serve, Murray wrapped up a straight-sets victory.
“As the match went on I got more used to his game style and played better, I started to strike the ball cleaner,” said Murray afterwards. “I served well at the beginning of the match, which is something I’m going to need to do if I want to go deep in the tournament.”
On Centre Court, Rafael Nadal made short work of a potentially dangerous opponent in JapanÃ¢â‚¬â„¢s Kei Nishikori. The second seed successfully wrapped up the match without dropping a set 6-2 6-4 6-4.
Nishikori, 20, employed an increasingly rare serve and volley tactic, but was broken twice in the opening set by his Spanish opponent. A closer second set saw Nadal prevail with the Spaniard managing to secure the crucial break in the ninth game, successfully serving out the set.
Nadal immediately broke in the third and threatened to win the match at a canter. However with the scores at 3-2 and the world No.2 facing a break point, a deceiving forehand stroke by Nishikori outsmarted the 2008 Wimbledon champion.
Unsurprisingly Nadal hit back with renewed ferocity restoring his stranglehold on the third set and wrapped up victory in just over two hours.
Next on Centre was No.6 seed Robin Soderling, who continued in the rich vein of form which saw him reach the final of Roland Garros. The Swede made short work of Robby Ginepri sealing a 6-2 6-2 6-3 victory in just under an hour and 20 minutes.
Tuesday’s seeded casualties included 19th seed Nicolas Almagro who was beaten by ItalyÃ¢â‚¬â„¢s Andreas Seppi in straight sets 7-6 (4) 7-6 (7) 6-2. On Court 5, 24th seed, Marcus Baghdatis exited SW19 at the hands of Slovakian Lukas Lacko losing 6-3 2-6 6-3 6-1.
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Lucas Torreira