The final composition of the Lower House has not emerged, but it is clear Abbott has stamped a new authority on his leadership.
The latest Electoral Commission count gave the Coalition 88 seats to Labor's 57 with another seat likely to be added to the new Government's column.
Greens MP Adam Bandt defied predictions to keep his Melbourne seat. North Queensland MP Bob Katter was returned for his new Australian Party and independent Andrew Wilkie retained his Tasmanian seat.
Abbott may yet lose frontbencher Sophie Mirabella to an independent rival, and mining magnate Clive Palmer yesterday appeared likely to win the Queensland seat of Fairfax. His United Party was also close to taking the seat of Fisher previously held by Liberal-cum-independent Speaker of the House Peter Slipper.
The Senate is a confusing mix that will not be sorted for days, at least. The largest groupings will be the Coalition and Labor, whose ranks now include the nation's first female indigenous parliamentarian, former Olympian Nova Peris.
The Greens appeared to have taken 10 seats, with hopes of more, and South Australian independent Nick Xenophon has won another term.
The mix could include One Nation founder Pauline Hanson and others from contenders including Palmer's United Party, the Sports Party, Bob Katter's Australian Party, Family First, and the Australian Motoring Enthusiasts.
This could be a better outcome for Abbott than the present Senate, in which the Greens hold the whip hand. The new Senate that will convene next July will potentially allow him to bide his time and navigate legislation with right and centre-right minnows.
This eases the prospect of the nation being sent back to the polls for a double dissolution election, a gamble Abbott was prepared to contemplate if key legislation - notably his repeal of the carbon tax - was blocked in the Upper House.
Depending on the plasticity of new senators, Abbott will move fast to implement the cuts and promises he made to repair the budget and boost its bottom line by A$6 billion ($6.88 billion) over the next four years.
His measures, many of which will be opposed by Labor and the Greens, cover climate change, the environment, renewable energy programmes, pruning the public service, cutting funds to major urban rail projects and the car industry, and slicing A$4.5 billion from foreign aid.
But Abbott has been warned by business and economists to be gentle with an economy battered by global pressures and a fragile domestic fiscal picture. While income from China's resource boom is cooling, the cost of funding government programmes is rising.
Abbott also faces unions concerned at a likely easing of industrial laws and conditions, and determined to hold him to his promise that no worker would be worse off under a Coalition Government.
Abbott also needs to rapidly come up to speed on foreign policy, with briefings on immediate concerns including the Syrian crisis and relations with Indonesia.
And in the background will be demands for a bigger say from junior Coalition partner the Nationals, who returned their best result in years.
National leader Warren Truss will become Deputy Prime Minister and he wants more portfolios.
Abbott started his first day in the job with an early Lycra-clad bike ride with friends.
His New Zealand-born wife Margie popped out for a few groceries, still coming to terms with looming changes to family life."It's a little surreal," she told reporters.
Abbott's plan: What's in store for Australia
The economy
Cuts and savings to boost the budget bottom line by A$6 billion ($6.9 billion), but no promises on the timing for a return to surplus.
Defence
Lift military spending to 2 per cent of gross domestic product within a decade, further tighten the US alliance.
Asylum seekers
Keep existing harsh measures, plus turning boats back under a new multi-agency taskforce led by a three-star general, buying small boats in Indonesia, imposing mandatory behaviour requirements, removing access to legal aid, and reintroducing three-year temporary protection visas for those found to be refugees.
Climate change
Axe Labor's carbon emissions trading plan, replacing it with other measures such as soil sequestration of carbon.
Education
Maintain Labor's reform funding for four years but dump its schoolkids' bonus, give more control to local communities, help state schools go private if they want, push foreign languages, especially Asian, and provide loans for apprentices to buy tools.
Broadband
Replace Labor's A$37.4 billion fibre optic network with a cheaper, slower alternative using existing copper-based links.
Industrial relations
Soften existing laws, impose greater controls on union access to worksites, allow employers and workers to negotiate individual deals outside existing enterprise agreements, and provide six months' paid leave for new mothers on full pay up to A$75,000.
Business
A 1.5 per cent in company tax offset by a levy to fund parental leave, provide new help for small business, cut aid to the car industry by A$500 million and review future funding for the sector.
Unemployment
A A$2500 bonus for dole recipients if they find work for a year, increasing to A$4000 if they stay off welfare for two years, with A$6000 for long-term unemployed who move to regional areas to work, or A$3000 for a shift to the cities.
