The governing New Patriotic Party lost at least half a dozen seats it held after the last election to Mills's National Democratic Congress (NDC), including that of Stephen Asamoah-Boateng, the information minister .
The NPP dominated the outgoing parliament with 128 of the 230 seats.
Samia Nkrumah, daughter of Ghana's independence leader Kwame Nkrumah, won a parliamentary seat in the family's home area of Jomoro, in Western Region.
Elections experts said the lead may switch back and forth between the candidates as more results come in from their respective regional strongholds outside Accra, the capital.
Six other presidential candidates shared the remaining votes.
John Kufuor, the outgoing president, steps down in January after serving the maximum two terms.
His successor takes over as Ghana looks to an era of greater prosperity when offshore oil comes onstream in late 2010.
The Electoral Commission and observers said turnout was high and voting had generally been calm despite isolated violence and long delays in some remote islands in Lake Volta due to problems delivering voting materials by helicopter.
Britain's Baroness Valerie Amos, leading an election monitoring team from the 23-nation Commonwealth, said Sunday had been "a good day for Africa".
"Most of the recent news about elections in Africa has not projected the continent in a good light," she said in a statement.
The Electoral Commission is due to announce the official result by the middle of the week, but media in Ghana are permitted to announce provisional results as posted outside polling stations.Second handover
The election is the second handover of power through the ballot box since Ghana introduced multiparty democracy in 1992.
Kufuor won the previous election in 2004 in the first round with 52.45 per cent of votes, against 44.64 per cent for Mills.
In 2000, he won power in a run-off, also against Mills, after Jerry Rawlings, a firebrand former coup-leader, stepped down.
Kufuor's centre-right administration has seen the economy grow by over 5 per cent annually in recent years and in 2007 launched black Africa's first Eurobond outside South Africa.
The former British colony is the world's second biggest cocoa grower and Africa's second-largest gold miner.
But many Ghanaians say the increased national wealth has passed them by, while critics say the government has done too little to combat widespread corruption and drug smuggling.