The current world number six proved to be too strong for his Slovakian opponent during the first two sets as he ran out 6-1 6-3 victor.
However, Beck provided a lot more resistance during the third set by breaking Tsonga at the first time of asking.
Tsonga responded with a break of his own to level up the scores at four games apiece, which eventually resulted in the set heading into a tie-break.
Beck committed a number of unforced errors during the breaker, which allowed Tsonga to secure his slot in the next round with a 7-2 triumph.
He will now face Martin Klizan for a place in round three.