Australia scored 207 for three in reply to Zimbabwe's 205 for nine to win with 10.2 overs to spare.
"We were a bit rusty in the field, and with the ball, but we batted really well," said Ponting. "We weren't as sharp as we could have been in the field.
"A lot of the guys have (not) played cricket for a couple of months, so it was a good game to get under our belt. We should do better next time around."
Ponting led Australia to victory with 91 from 93 balls, stroking eight fours and three sixes before he was dismissed by a brilliant one-handed diving catch by Vusi Sibanda at long-on.
"It got a bit tight, and I needed the last nine runs left in the game (to reach a century)." Ponting said. "But I got out to a pretty good catch so I can't complain."
Zimbabwe captain Tatenda Taibu said he was satisfied with his team's overall performance.
"We were looking to get 230 plus," Taibu said. "I asked my batsmen to give it their best shot, and I thought they did that.
"(Brendan) Taylor (who scored 59) showed a lot of guts and I was happy with the way he played.
Taibu, however, said he felt the bowlers needed some work before the second match in Harare on Thursday.
"Our bowling was a bit shaky at the beginning and we could still improve."
