The competitors were well matched in the early stages of the game, with the first set going by the way of serve until the world number six snatched the first break and took the lead in Melbourne.
It looked as though Tsonga's Uzbekistani opponent was in for a quick defeat after the sixth seed broke Istomin's first game of the second set. However, the 25-year-old instantly broke back in order to level the score.
The match became increasingly harder for Tsonga as Istomin continued to push the Frenchman and managed to draw level on sets with the chance to take the lead.
While the Uzbekistan pro tried to put pressure on Tsonga, the 26-year-old was able to withstand Istomin's game and snatch the third set with a break of serve.
Both opponents were evenly matched in the fourth set until last year's Wimbledon semi-finalist edged Istomin with a break of serve and looked certain to clinch the match. However, Istomin failed to give up and fought back from 5-2 to draw level.
While the unseeded pro refused to back down, Tsonga proved his world ranking by seeing through the set and winning the contest.
The Frenchman will face Ricardo Mello in the second round.