* Military deployed in rare move to clamp down on unrest
* Police use rubber bullets, stun grenades on protesters
* Ruling ANC wins more than 60 pct of vote in election
* Zuma to make post-election speech at 1600 GMT
(Updates with military confirmation, details)
JOHANNESBURG, May 10 (Reuters) - South Africa deployed its armed forces overnight to quell post-election unrest in a Johannesburg slum and police arrested 59 people as the ANC government clamped down on disorder following its victory at the polls.
While the African National Congress remains popular with South Africa's black majority 20 years after dismantling white apartheid rule, there is rising discontent among millions stuck in grinding poverty.
Violent protests - often over lack of access to running water or electricity - are common in South Africa's impoverished black townships, although military intervention has been rare.
On Friday, police used rubber bullets and stun grenades to disperse demonstrators who burned tyres and barricaded roads in the Alexandra township north of Johannesburg, spokesman Brigadier Neville Malila said.
But the military was deployed to back up the police when the security situation deteriorated overnight and will remain "as long as required", army spokesman Brigadier General Xolani Mabanga said.
Malila said Alexandra was "calm this morning", and no further incidents were reported.
The ANC won the 2014 national election with 62.16 percent of the votes, according to a provisional tally of Thursday's balloting. Official numbers were due to be announced later on Saturday and President Jacob Zuma was expected to address the nation at 1600 GMT.
South Africa's fifth post-apartheid election came off largely peacefully at the thousands of polling stations nationwide, with the turmoil in Alexandra the most significant election-related violence.
Politician Julius Malema, whose leftist Economic Freedom Fighters took third place in the election, called for calm.
"People in Alexandra, we call on you to accept defeat. Do it in a dignified manner," he said at a news conference. "Don't put South Africa into ashes because of election outcomes."
ELECTORAL OFFICE TORCHED
As many as 400 people had gathered on Friday outside a court in Alexandra to demand the release of other protesters arrested a day earlier, police spokesman Malila said.
On Thursday more than 30 people were detained after an electoral commission office was torched in Alexandra. Both groups of detainees were due to appear in court on Monday.
By calling in the army, the African National Congress government appeared to be taking a harder tack against public unrest than it has in the recent past.
When violent labour unrest swept through South Africa's platinum-mining belt in 2012, the government put the army on standby but did not dispatch it.
Burdened with sluggish economic growth and damaging strikes in his first term, the scandal-plagued Zuma is at pains to soothe investor concerns about Africa's most sophisticated economy and push through pro-business reforms.
Over the last year he has devoted less and less time to the wishes of unions, whose long walkouts have hit confidence in the economy. Zuma hinted this week that the ANC needed to take a more pro-business stance, accusing the main platinum union of irresponsibility for dragging out a four-month wage strike.
(Editing by Mark Heinrich)