The 27-year-old Barcelona star`s shot from an angle on 47 minutes in Jeddah came back off the far post before hitting Hassan Muath Fallatah for an own goal.
Suarez was replaced with 20 minutes to go but his hopes of a winning international return were ruined by Naif Hazazi`s last minute equaliser for the former Asian champions.
Although still serving a nine-match competitive international ban for sinking his teeth into Italy`s Giorgio Chiellini at the World Cup, Suarez is allowed to play in friendlies.
Suarez, whose club ban ends in two weeks when Barcelona face bitter rivals Real Madrid, could have scored just before coming off when he pounced on a dreadful back pass.
But with only goalkeeper Waleed Abdullah to beat, he tried to dribble past the shot-stopper and was tackled.
Asian champions Japan gave Javier Aguirre his first win with a laboured 1-0 victory over Jamaica while Australia struggled to a 0-0 draw in sweltering Abu Dhabi.
Japan, like Australia, building towards the Asian Cup in January, squandered several chances against Jamaica in Niigata but an own goal from Nyron Nosworthy in the 16th minute proved decisive.
Japan were beaten 2-0 by Uruguay and were held 2-2 by Venezuela last month in their first two games under Mexican coach Aguirre, who took charge following the side`s World Cup flop in Brazil.
“I feel calm, relaxed as always. We created five or six more chances to score, which was pleasing,” said Aguirre.
Japan will need to improve before a glamour friendly against Brazil in Singapore on Tuesday.
“We won`t get as many opportunities against Brazil as we did today,” added Aguirre. “We will have to be more clinical when chances come our way.”
In humid Abu Dhabi, Australia were held 0-0 by fellow Asian Cup finalists United Arab Emirates.
Alex Wilkinson needed to clear Ali Ahmed Mabkhout`s attempt off the line in the first half while Trent Sainsbury missed Australia`s best chance late in the game after being teed-up by Tim Cahill.
In Wuhan, China`s build-up for the Asian Cup continued with a 3-0 over Thailand thanks to a second-half own-goal from Thai goalkeeper Sinthaweechai Hathairattanakool, Sun Ke and Yang Xu.
In Muscat, World Cup quarter-finalists Costa Rica edged Oman 4-3 with Alvaro Saborio, John Jairo Ruiz, Juan Bustos and David Ramirez on target while Saleh Raed, Mohammed al-Seyabi and Emad al-Hosani replied for the Gulf state.
Uli Stielike`s first game as South Korea coach saw a 2-0 win over Paraguay in Cheonan with goals from Kim Min-Woo and Nam Tae-Hee in the space of five first-half minutes.