Sanchez sent a corner from the left side which keeper Mohammed al Owais swiped at but missed and Suarez easily tapped home to become the first player from his country to score at three World Cups.
On Wednesday, Saudi Arabia will face off with Uruguay, who are hoping to appease some worries after only beating Egypt 1-0 thanks to a late goal.
A victory may cement Uruguay's position as the group's leader, lining it most probably for a tough second-round clash against Spain or Portugal.
Three goals in the first 20 minutes of the second half virtually ended Egypt's World Cup.
The two-time world champions can book their place in the last 16 with victory, while defeat would see Saudi Arabia eliminated after their 5-0 opening thrashing by Russian Federation, while also knocking out Mohamed Salah's Egypt.
"This World Cup is proving that what matters most is the result, and we're very proud to have reached the last 16 for the third time in a row".
Theranos founder Elizabeth Holmes charged with fraud
The DOJ claims that Holmes and Balwani knew Theranos' product wasn't as effective as the company had been describing. The criminal charges came after Holmes in March settled civil fraud charges brought by the U.S.
While Uruguay has done just enough to get past two lackluster opponents in its two Group Stage wins, there's a sense that we haven't seen the best of the South American side, that is one of just five countries to have won the World Cup a couple of times.
Another alternative to watch Saudi Arabia vs Uruguay is to try out the FuboTV 7-day free trial.
Saudi Arabia have conceded 14 headed goals at the World Cup and it could have been 15, Martin Caceres heading over in the 68th minute from another Sanchez delivery.
Uruguay beat a 48-year curse of failing to win a World Cup finals opener on Friday, but needed an 89th-minute header to do so.
Paris Saint-Germain striker Edinson Cavani started alongside Suarez as the pair look to add to their combined tally of 93 worldwide goals.
Saudi Arabia also had to play most of the match without trusted midfielder Taisser Aljassam, who limped off before halftime with an injury after lunging forward for a challenge.