Bonmati's early opener in the last-16 tie in Auckland was cancelled out by a spectacular own goal from Laia Codina, but Alba Redondo restored Spain's lead and Bonmati scored again to make it 3-1.

Codina then made up for her error by getting her team's fourth before the interval, and Jennifer Hermoso made it 5-1 in the second half in front of 43,217 fans, a new record crowd for a football match in New Zealand.

The result was a huge boost to Spain following their 4-0 defeat by Japan in their last group game, and the performance justified coach Jorge Vilda's decision to leave Alexia Putellas out of his starting line-up.

The reigning Ballon d'Or winner is still recovering fitness following a serious knee injury and could yet play a key role later in the tournament, but made just a cameo here off the bench.

Spain can now look forward to playing in the last eight of the World Cup for the first time when they face the Netherlands or South Africa in Wellington next Friday.

They were simply a class above a Swiss team who had reached the last 16 without conceding a goal but whose exit means they have still never won a major tournament knockout game.

Putellas was dropped as Vilda responded to the chastening Japan defeat by making five changes to his line-up.

Most notably, Misa Rodriguez made way in goal for Cata Coll, a back-up at her club Barcelona. Codina also came into central defence for her first appearance at the World Cup.

- Farcical own goal -                  

The Spain line-up featured six players from UEFA Champions League winners Barcelona, despite another being left on the bench in Putellas.

And it was one of the Barcelona contingent who opened the scoring inside five minutes as Bonmati slotted in after taking a lovely touch to set herself up.

That came after Redondo's effort from a Salma Paralluelo cross had been touched onto the post by goalkeeper Gaelle Thalmann, and Switzerland had conceded for the first time at this World Cup.

They were gifted an equaliser on 11 minutes as Codina, not far inside her own half, played a ball back towards her own box without looking up, and beat Coll for a farcical own goal.

Yet Spain were back in front soon after as Bonmati glanced on a cross from the left by Ona Batlle and Redondo arrived to head home.

Bonmati was running riot and was denied another by a good Thalmann save before she made it 3-1 in style in the 36th minute.

Redondo's header from Paralluelo's cross was blocked but the ball fell to Bonmati who wrong-footed the Swiss defence with a turn reminiscent of Johan Cruyff before finishing.

Codina then poked in another in a goalmouth scramble at a corner, and it was 4-1 at half-time without Switzerland having had an attempt on goal.

The fifth arrived 20 minutes from time as Bonmati pounced on a slack pass out by Switzerland and played in Hermoso to score.

Bonmati was removed shortly after and Putellas was sent on for the final quarter of an hour, by which time Spain's thoughts had turned to the next round.