Suarez celebrated his 100th worldwide cap with the only goal in a 1-0 victory over Saudi Arabia at the Rostov Arena.
Al-Owais - winning only his second cap after replacing Abdullah Al-Muaiouf in goal - completely missed a floated Carlos Sanchez corner and Suarez tapped in his 52nd worldwide goal unmarked at the back post.
It was the Barcelona striker's 52nd goal for his country in that century of games. A Luis Suarez goal in the first half off a corner kick proved to be difference, but it was a proud and positive performance from the Saudi Arabians, who gave Uruguay more trouble than expected.
Saudi Arabia, thrashed 5-0 by Russian Federation in their opener, offered more resilience against Uruguay but rarely threatened an unlikely draw and coach Juan Antonio Pizzi felt his players showed a significant improvement in their performance.
But he lamented his side's lack of firepower as they exited the World Cup after just two matches.
In truth, it was another stuttering display from Oscar Tabarez's Uruguay team.
"That's not the best game we've seen at this World Cup", admitted Drogba.
"Of course we demand a lot more from this type of player", Tabarez said at his post-match press conference.
"We forgot about it as soon as we got to the hotel", Saudi Arabia midfielder Taisir Al-Jassim told a news conference on Tuesday.
Fernando Muslera had to tip over a long-range drive from Hattan Bahebri, who then missed a fine chance in the box, as Saudi Arabia responded well to falling behind. You don't see 10-0 games at the World Cup anymore.
"I do fancy them in this tournament", said Neville.
"We have to fine-tune a few things, we have to work on a few aspects". This just goes to show that fans want good football, boring play styles and a lack of chances really don't go down well, so hopefully, there aren't too many games like this one moving forward!
Pizzi denied reports that Saudi officials had vetoed four players from the starting lineup on Wednesday.