Khoukhi rose highest to thump in Homam Ahmed's cross on 94 minutes and cancel out a first-half Breel Embolo penalty, leaving the Swiss stunned and rueful after failing to convert 26 attempts to Qatar's seven.

The result left Group B wide open, with all teams locked on a point each after co-host Canada's 1-1 draw with Bosnia and Herzegovina.

Qatar will be easily the most pleased among two sides, four years after its 2022 debut fell flat with a winless elimination on home soil.

The entire Qatar squad stormed on to the pitch in ecstasy after Khoukhi's header fizzed by Swiss goalkeeper Gregor Kobel, giving Spaniard Julen Lopetegui a landmark result coaching his first FIFA World Cup match.

"We achieved one dream when we arrived here, to be here, and now today is another little dream," Lopetegui said. "And we have the right to continue having the dream."

Qatar goalkeeper Mahmoud Abunada was also naturally thrilled, having fouled Remo Freuler to hand the Swiss their 17th-minute penalty.

"This is the first point in the history of the Qatari national team. Praise be to God in all circumstances," Abunada said.

"Honestly, the match was played with great determination from everyone."

Switzerland may feel the footballing gods deserted it having seen chance after chance go begging, with Dan Ndoye particularly wasteful in the first half.

It was all set up for the group favourite, though, when Abunada smashed into Freuler in the six-yard box.

Freuler ran on to a header by Embolo in the area, dinked the ball goalwards past Abunada and was met heavily by the goalkeeper, who came off second best in the clash.

Referee Said Martinez pointed straight at the spot but it took a long video assistant referee (VAR) check to confirm the penalty while a prone Abunada, who was booked for the challenge, was attended to by medical staff.

While Michel Aebischer racked up a sixth Swiss shot on goal, stopped on the line deep into first-half stoppage-time, Qatar's attackers were left with scraps.

The Asian champion's dangerman Akram Afif was well-shackled but found space down the flank late in the half to set up Edmilson for a one-time shot saved by Kobel.

With Qatar camped in rows in front of goal, the match meandered in the second half and a raft of substitutions on both sides of the drinks interval did nothing to break the stasis.

That was until Ahmed found Khoukhi with a sumptuous cross to snatch the draw, leaving clumps of thobe-wearing Qatar fans jumping in the stands.

Switzerland may still fancy its chances of getting out of the group but the road ahead is rockier and its inability to seal the win will be a concern for coach Murat Yakin.

It faces Bosnia and Herzegovina at Los Angeles Stadium on Friday (AEST), while Qatar, which defended doggedly to thwart the classy Swiss, heads north to meet co-host Canada in Vancouver on the same day.

Despite the official attendance of 67,966, there were banks of empty seats at the 70,000-seat home of the NFL's San Francisco 49ers.