As acting President Nicolas Maduro visited Chavez's hometown of Sabaneta in the west, opposition leader Henrique Capriles was heading to the eastern state of Monagas at the start of the short campaign ahead of the April 14 vote.
"The bus that is this fatherland has just one driver, and I am your man," insisted Maduro, playing up his humble past as a bus driver and union organizer.
Both candidates have vowed to canvass all 23 states over 10 days in what is shaping up to be an emotionally-charged election to replace the charismatic Chavez, who led the oil-rich nation for 14 years.
The rivals have traded barbs for weeks since Chavez lost his battle with cancer on March 5, leaving the nation split between supporters of his self-styled socialist revolution and opponents hoping for change.
Maduro, 50, a former foreign minister and vice president, was joined by hundreds of supporters, officials and Chavez relatives as he visited the late president's family home, now a local headquarters of the ruling PSUV party.
"We will fulfill the will and legacy of president Chavez," an emotional Maduro said, describing the house as the "cradle of the Bolivarian revolution."
"We feel comandante Chavez within us, like a father. We come to make a commitment with this land that saw his birth, pledge to never fail him and build socialism to its fullest development," he said.
Maduro has a double-digit lead over Capriles in opinion polls, thanks in part to a wave of sympathy after the death of Chavez, who was immensely popular among the poor and other beneficiaries of his oil-funded social programs.
Chavez brought free health care and subsidized food programs to poor areas while reducing poverty, but the opposition points to Venezuela's high murder rate, soaring inflation and shortages of basic goods.
"We are all Chavez; and now we are all Nicolas," said computer technician Francisco Martinez, echoing slogans commonly heard on state television.
Capriles, the telegenic 40-year-old governor of Miranda state, gave Chavez his biggest ever electoral challenge in October elections but still lost by 11 points.
While Maduro was on Chavez's home turf, Capriles rallied thousands of supporters to formally launch his campaign in the eastern city of Maturin.
"There is hope here. There is faith here. And there is also going to have to be bravery here," Capriles said under a scorching sun amid a sea of red, blue and gold flags.
"I am going to give it all ... to move this country forward, in the coming days and in the coming years. But I want you to do the same along with me," Capriles urged.
Chavez was unable to attend his January 10 swearing-in ceremony because he was receiving treatment in Cuba at the time, part of a nearly two-year battle with cancer that saw him shuttle back and forth to Havana.
The opposition was further weakened after a big defeat in regional elections in December that left it with only three of 23 gubernatorial seats.
Even in death, Chavez is casting a huge shadow over Venezuela, with a myth building around his larger-than-life personality. This could benefit Maduro, who constantly lionizes his mentor.
Maduro has compared Chavez to South American independence hero Simon Bolivar, referring to him on Tuesday as a "prophet," a "giant of the fatherland" and the "supreme commander."
Adopting Chavez's man-of-the-people style, the acting president hugged and greeted thousands of supporters, rode a Jeep in the scarlet red of "Chavismo" and crooned along to local music known as llano.
Many of his supporters believe Capriles, a governor and attorney, is better trained and more up to the executive post than Maduro.
"Even if Chavez said people should vote for Maduro, he is not prepared to be president. In his speeches all he talks about is Chavez. He has no policies," said Ana Vazquez, 78, who rallied along with her daughter and granddaughter.
The National Electoral Council, which the opposition accuses of being biased towards the ruling party, has called for a peaceful campaign in the politically polarized nation.
"This campaign will take place in a delicate emotional context, so we urge all parties to ... avoid expressions that could strain the electoral environment," said council president Tibisay Lucena.