Argentina striker Martinez lashed home his fourth goal of the season in all competitions on the hour mark after a poor clearance from Zeki Celik to give Inter a hard-fought win at the Stadio Olimpico in Rome.
Lautaro confirming his intention to stay at Inter is a huge boost for a club which headed into the close season in uncertain mood after a sudden change in ownership.
It’s a huge relief for the Inter Milan marksman, who had experienced a miserable 18 months.
With Messi sidelined after complaining of a sore right hamstring, and coach Lionel Scaloni serving a one-game suspension, Argentina made nine changes to their starting XI at the Hard Rock Stadium.
Just as it looked like Argentina would be made to rue their missed chances substitute Martinez pounced on a rebound from a corner and lashed home a right-footed shot in the 88th minute to ensure victory and a top-two spot in the group for the defending champions.
Lautaro Martinez, this season's Serie A top scorer, put Argentina ahead with a penalty kick in the 39th minute before netting his second from a Messi pass after the break.
"Now, I feel like crying because we worked so hard, suffered so much, we deserved this joy," the 26-year-old told DAZN.
Angel Di Maria, Alexis Mac Allister and Lautaro Martinez rescued Argentina on Tuesday as the world champions came from behind to beat Costa Rica 3-1 in an international friendly in Los Angeles.
Martinez has gone 16 consecutive games without scoring a goal, spanning a total of 772 minutes.
Argentina forward Martinez glanced home the decisive goal in the 14th minute of an action-packed contest in Florence in which Nicolas Gonzalez wasted a late penalty for the hosts, who had Inter on the back foot for much of the game.
Lautaro Martinez shot Inter Milan to a third straight Italian Super Cup after netting in the final moments of Monday's 1-0 win over furious Napoli in Riyadh.
Inter's dynamic attacking duo made sure their team took full advantage of closest rivals Juventus only drawing at Genoa on Friday to put daylight between Simone Inzaghi's side and the rest of the chasing pack
Lautaro Martinez ensured that Inter Milan kept hold of their two-point lead at the top of Serie A as he struck in Sunday's scrappy 1-1 draw at closest rivals Juventus.
Lautaro Martinez and Marcus Thuram have rapidly struck up a formidable attacking partnership which will lead Inter Milan into Tuesday's Champions League Group D clash with Salzburg.
Argentina striker Martinez nodded home his 11th league goal of the season in the 67th minute of a straightforward win in Turin as Inter went one point ahead of AC Milan, who host third-placed Juventus on Sunday night.
Bologna fought back from two goals down to snatch a 2-2 draw with Inter Milan at the San Siro in Serie A on Saturday after early goals from Francesco Acerbi and captain Lautaro Martinez had put the hosts in command.
Inter rebounded from their first loss of the season midweek against Sassuolo thanks to a sensational second-half display from Martinez.
Lautaro Martinez struck late to snatch last season's Champions League runners-up Inter Milan a 1-1 draw at Real Sociedad on Wednesday, denying the Spanish side a triumphant return to the competition after a decade away.
The 25-year-old will pair up with either Edin Dzeko or Romelu Lukaku in attack as his team face Manchester City in Istanbul as big underdogs