Four years ago the Central Americans denied Switzerland a place in the knockout rounds by holding out for a 0-0 draw but two first-half goals from the impressive Bayern Munich player gave Honduras a mountain to climb.
Coach Luis Suarez's team fought hard to get back into the game even though they had no chance of progressing but a third goal from the midfielder killed their hopes.
Ottmar Hitzfeld's team, sixth in the FIFA rankings, came into the game level on points with Ecuador in Group E, three points off leaders France, knowing a victory would likely see them progress.
They went close to scoring with their first attack of the game, when young forward Josip Drmic burst forward and centred for Shaqiri but goalkeepr Noel Valladares blocked his shot.
In just the sixth minute Bayern Munich midfielder Shaqiri found the target with an unstoppable left-footed strike from just outside the area that flew past a helpless Valladares and into the top corner.
Honduras, who came into game on the back of two defeats, enjoyed long spells of possession but did not threaten Diego Benaglio's goal and just after the half-hour the Swiss doubled their lead following a swift counter-attack.
Victor Bernardez made a mistake in midfield and Drmic raced forward before playing in Shaqiri, who kept his composure with just the goalkeeper to beat, slotting the ball to his left.
He became the first Swiss player to score multiple goals in a World Cup match since 1954.
Honduras came out of the blocks impressively after the half-time break and Jerry Bengtson nearly pulled one back with an attempt at a diving header but failed to make contact.
Swiss defender Ricardo Rodriguez was then forced into a goal-line clearance after Bengtson beat the Swiss keeper and about 15 minutes later Fabian Schaer also had to clear off the line.
But Switzerland killed the game 20 minutes from time.
Drmic, enjoying his role on the left, beat Bernardez and again found Shaqiri, who was unerring in his finish.
Despite their lofty current ranking the Swiss, playing their 10th World Cup finals, last reached the quarter-finals in 1954 when the tournament was held on home soil.
They will meet Argentina in Sao Paulo on Tuesday while France, who topped the group after a 0-0 draw with Ecuador, will play Nigeria in Brasilia the day before.