The hosts' real test is expected to come against Asian champions Sri Lanka, the third team in the series in which all sides face each other twice with the top two playing in the October 16 final.
Pakistan has never won a home One-day tournament after failing in the 1987 and 1996 World Cups and in a tri-series in 1994 and a four-team tournament in 1997.
"I am confident that we will win our first home One-day title and although we know Zimbabwe is ranked outsiders due to missing their key players we will not take them lightly," said Inzamam, whose side has shown improvement under new English coach Bob Woolmer.
Since Woolmer's induction in June this year, Pakistan won four of their five matches in the Asia Cup in July in Sri Lanka followed by a runners-up finish to Australia in a tri-series in Amstelveen, Holland.
They also came close to beating Australia in a one-off limited overs international at Lord's before losing to the West Indies in the semi-final of the International Cricket Council (ICC) Trophy in England.
"We have shown improvement but the real thing is the winning finish where we have shown weakness and need to come over that problem," said Inzamam.
"We lost to Sri Lanka in the Asia Cup and now need to beat them to win the title," said Inzamam, who last week became only the second batsman besides India's Sachin Tendulkar to score 10,000 one-day runs.
Pakistan have included two uncapped players in batsman Bazid Khan, son of former captain Majid Khan, and pacer Rao Iftikhar in their 15-man squad for the series.
Zimbabwe, facing a huge turmoil after a rebellion by 15 white players including captain Heath Streak and suspension of their Test status, drew a two-day tour opener in Pakistan before suffering innings defeat in a four-day match last week.
"We are a young team but we can take inspiration from our good showing against Sri Lanka in England earlier this month where we gave them a run for their money," said Zimbabwe captain Tatenda Taibu, who became the youngest ever captain at international level at 20 in April this year.
Following a players' strike over racisim in selection in April, Zimbabwe lost all their five One-day games on home grounds to Sri Lanka besides suffering the ignominy of being dismissed for One-day cricket's lowest score of 35.
They also lost both the Tests to Sri Lanka by innings followed by another 5-0 One-day series routing by Australia.
Their defeats prompted the ICC to suspend their Test status until the end of this year and form a two-member jury to probe racism allegations in Zimbabwe cricket which starts on Wednesday.
"We have set targets for ourselves so its a process of learning to overcome what happened in the last six months," said Taibu.
Pakistan again faces Zimbabwe in the second match at Peshawar on October 3 before thier October 6 game against Sri Lanka who arrive on Monday.
Pakistan: Inzamam-ul Haq (captain), Shahid Afridi, Yasir Hameed, Bazid Khan, Salman Butt, Shoaib Malik, Yousuf Youhana, Younis Khan, Moin Khan, Misbahul Haq, Abdul Razzaq, Shoaib Akhtar, Mohammad Sami, Rana Naveedul Hassan, Rao Iftikhar.
Zimbabwe: Tatenda Taibu, Brendon Taylor, Vusimuzi Sibanda, Dion Ebrahim, Mark Vermeulen, Stuart Matsikenyeri, Alestar Maregwede, Mluleki Nkala, Elton Chigumbura, Edward Rainsford, Tawanda Mupariwa, Prosper Utseya, Douglas Hondo, Tinashe Panyangara, Graeme Alexandar Cremer
Umpires: Mark Benson (ENG), Nadeem Ghauri (PAK)
TV umpire: Asad Rauf (PAK)
ICC match referee: Jeff Crowe (NZL)