The sixth-seeded Pennetta used two straight aces to clinch the win.
''She fights until the last point,'' Pennetta said. ''I went for the last points on my serve. I did not want to get into a rally.''
Pennetta, who had to go through qualifying for this tournament last year, won the first four games against Koukalova.
''I tried to be aggressive and stay close to the baseline,'' Pennetta said. ''She's a really good player. Sometimes it looks as though she's not trying, but that's the way she plays. You never know what she's going to do.''
Pennetta will meet American Alison Riske in the second round. The two have never played one another.
Riske beat Casey Dellacqua of Australia 6-1, 6-4 in her first-round match. Dellacqua broke Riske's serve in the first game, but the 43rd-ranked Riske won the next six games to clinch the first set.
At 4-4 in the second set, Riske broke the 30th-ranked Dellacqua's serve then closed out the match.
Giorgi had four aces and only one double-fault in needing just 24 minutes to win the second set.
Ekaterina Makarova of Russia beat Roberta Vinci of Italy 6-3, 6-3. The 18th-ranked Makarova has reached the semifinals of her last two tournaments in Washington and Montreal.