Williams, who beat sister Venus in last year's final here, has yet to drop a set in the first three matches of her title defence and she was far too strong for world number 46 Cibulkova.
The American top seed will face either 2004 Wimbledon champion Maria Sharapova or Barbora Zahlavova Strycova in the next round.
The three-time champion clearly has no intention of expending unnecessary energy in the first week of the tournament.
Serena had lost just five games in the previous two rounds at the All England Club - with her victory over Anna Chakvetadze in the second round taking just 49 minutes.
She had won the opening set in both her opening two matches with dropping a game and once again she set out to shatter her opponent's resolve in the first set.
An ace with the first serve of the match and a break of the Cibulkova serve in the following game emphasised Serena's desire to go for the jugular straight away.
Serena looked impregnable on serve and, with the 21-year-old Cibulkova looking overawed by the Centre Court occasion, it was no surprise that the world number one took the first set in just 18 minutes.
Cibulkova gradually found a little more confidence in the second set and began to at least make Serena break sweat.
The Slovakian fended off match point as she held serve for 5-5. But Williams was never likely to be held up for long and she broke in the 12th game to seal her path into the second week of the tournament.