It was a gesture for the television cameras, and it preceded the real business of yesterday: two hours of talks between Ms Clark, the Labour Party leader, and Mr Anderton, who heads the left-wing Alliance, aimed at hammering out a modus vivendi that will enable them to put aside their differences and govern New Zealand as a centre-left coalition.
Together, Labour and the Alliance command a majority of six seats in the 120-seat parliament after Jenny Shipley's ruling Nationals were ousted by voters seeking a change of direction after nine years of conservative rule.
It does not sound like much, but in New Zealand terms it amounts to a virtual landslide victory. Under a German-style electoral system of limited proportional representation adopted in 1996, one-party rule has become a thing of the past, and government is all about deals and compromises.
Mr Anderton and his colleagues were once members of a left-wing faction of the Labour Party, but they walked out a decade ago because they disagreed with radical free-market reforms undertaken by the last Labour government under David Lange.
The concern in New Zealand is that, for all the kissing and making up that is going on at the moment, a centre-left government would be vulnerable to the same policy splits.
There is also the personal animosity between Ms Clark, Labour leader for the past six years, and Mr Anderton. The two were once good friends, so much so that Ms Clark married her husband, Peter Davis, in Mr Anderton's backyard.
That was before Mr Anderton's own first marriage broke up - messily; Ms Clark was, and remains, close to his ex-wife. Relations were further strained after his daughter committed suicide. But 18 months ago, the two leaders acknowledged political realities and took the first tentative steps towards reconciliation.
After talks at the Grand Chancellor Hotel yesterday, Ms Clark - looking the worse for wear after four hours of sleep following a victory party in her west Auckland constituency - said she was confident a government could be sworn in by the end of next week.
Mr Anderton has said that there is "an enormous amount of goodwill" between him and Ms Clark.
Labour has promised a fresh start for New Zealand after 15 years of right-wing policies initiated by Mr Lange and continued by successive National Party administrations. Priorities include a higher tax rate for top earners, an increase in pensions and repeal of legislation curtailing workers' rights.
The National Party's defeat is expected to spark a leadership challenge to Mrs Shipley from her Treasurer, Bill English. Mrs Shipley, who spent yesterday at her home in the South Island town of Ashburton, reflecting on the roller-coaster of democratic politics, said with a sigh that she planned to spend more time with her electorate.
"I'm an optimistic person," she said. "I don't spend time dwelling on what could have been. I'm disappointed, but I'm going to make the best of it." Ms Clark expressed the hope yesterday that Labour's victory would halt the exodus of young New Zealanders to Australia and Europe and might even tempt some expatriates to return. "If we can rebuild an economy that creates more opportunities for skilled and educated people, I'm convinced we'll get them home," she said.