Saudi goalkeeper Waleed Abdullah did well to keep out substitute Augusto Fernandez and Messi who shares the Argentina record of 12 goals in a year with former striker Gabriel Batistuta.
"We didn't have a good match. We lacked spark and kept giving away possession," visiting right-back Pablo Zabaleta told Fox Sports television at the King Fahd stadium.
The 112th-ranked Saudis, coached by Dutchman Rijkaard who gave Messi his Barcelona debut in 2004, defended in numbers and frequently troubled Argentina with quick breaks.
The home team had the ball in the net when defender Mohammed al-Sahlawi headed a free-kick past goalkeeper Sergio Romero in the 28th minute but were unlucky to see a marginal offside decision go against them.
Messi has 12 goals in nine internationals this year and 31 altogether for Argentina.
Batistuta, who holds the overall record for his country with 56 goals, hit 12 in 1998.
"We deserved to win. In the second half we created six goal chances," said coach Alejandro Sabella whose Argentina team lead the South American World Cup qualifying table.
Messi's strike partner Sergio Aguero said: "The important thing is we didn't lose but it would have been nice to end the year with a win".
The Saudis, who had the clearer chances in the first half, went close from a 19th minute counter-attack but a weak shot by the nippy Naser al-Shamrani was palmed away by Romero.
Messi broke away on the right in the 42nd minute only to see his low cross intercepted by a defender just as midfielder Eduardo Salvio looked set to score.
In a flurry of action midway through the second half both sides cleared chances off the line and late pressure from Argentina, who played mostly at training ground pace, failed to yield a goal.
The Saudis usually had at least eight men behind the ball, giving the Argentine forwards little room.
Aguero was just wide with a shot from outside the box and substitute Franco Di Santo, making his debut, headed an Angel di Maria cross over the bar.
Argentina have won two and drawn two of their meetings with the Saudis.
