Youzhny, the 2004 champion and a two-time runner-up, won four consecutive points in the first-set tiebreaker and then took the last five games after both players held their opening serves in the second set.
The 29th-ranked Youzhny won his eighth career title in Zagreb, Croatia, in January but has not advanced past the second round in five events since losing to Roger Federer in the quarterfinals at Wimbledon.
"The first match at any tournaments is always not an easy one," Youzhny said. "When he (Pospisil) served well it was tough to receive. I've played few matches after Wimbledon and definitely lack practice."
Zemlja won five consecutive games in the first set and never faced a break in the second.
"It wasn't easy. Maybe it looked easy, but I was fighting throughout the match," Zemlja said. "I was trying to win every point, every game."