Suarez scored a free-kick from outside the box to give his side the lead before Messi's late intervention.
The sport had been dubbed by organisers as an essential second for Israel, following the cancellation of one other Argentina match a yr earlier after stress from pro-Palestinian campaigners.
Meanwhile in the UEFA EURO Qualifiers Spain beat Romania 5-0 while Italy thrashed Armenia 9-1.
The Argentine went past as many as six players from Uruguay and left fans in the awe of his genius.
Organisers dubbed it as a game about peace, but boycott campaigners called for it to be cancelled over Israel's treatment of the Palestinians.
"The footballers were very anxious, just like me and the coaching staff. We were sent images of missiles which were exploding in the air and we have not experienced that before", Tabarez said.
A ceasefire was declared on Thursday but remains fragile.
"In bringing perhaps the world's most famous athlete, Lionel Messi, to Israel, we are providing excitement for the entire country - for Muslim, Christian and Jewish citizens of Israel", he stated in a press release to AFP. On the pitch at occasions it felt just like the Messi present, with the gang chanting his identify and each mazy run greeted by vociferous cheering.
Israel considers Jerusalem its "indivisible" capital, when Palestinians claim the japanese section of the town - occupied by Israel in 1967 and afterwards annexed - as the cash of their long term state.
Five minutes later Suarez netted to put Uruguay back in front, and despite Argentina's attacks through Dybala and Aguero, Oscar Tabarez's side looked set to hold firm.
For the second time in just a few days Lionel Messi had on field "beef" with the opposition, this time almost coming to blows with Edinson Cavani.
He returned to the national team on Friday, scoring the winning goal in a 1-0 victory over Brazil.