France reached an unassailable 3-1 lead and will face either Belgium or 28-time champion Australia in the final. The Australians led 2-1 in Brussels before Sunday's reverse singles.
France qualified for its first final since losing to Switzerland in the title match three years ago.
Tsonga won his second point for France after defeating 22-year-old debutant Laslo Djere in straight sets on Friday to level the tie at 1-1. Two-time Grand Slam champions Nicolas Mahut and Pierre-Hugues Herbert then gave the hosts a 2-1 lead when they beat Filip Krajinovic and Nenad Zimonjic in the doubles match.
Tsonga was overpowered by his rival in the first set but improved and recovered in the second by upping his game when it mattered, after a double fault from Lajovic gave him an early break.
The third set was close with neither player giving an inch on the red clay of the Pierre Mauroy stadium. Lajovic was the first to crack despite saving two set points in the tiebreaker when he dumped a backhand return into the net.
Tsonga missed three break chances in the opening game of the fourth set but converted the fourth after Lajovic made two consecutive unforced errors, a double fault and a forehand in the net.
The Frenchman then held to love and broke again as Lajovic showed signs of fatigue following his five-set win over Lucas Pouille on Friday. Tsonga then served out the match.