Some 7.2 million people tuned in to the three-hour show, hosted by How I Met Your Mother star Neil Patrick Harris.
The telecast came second to an NBA finals game between San Antonio and Miami, watched by 11.6 million.
Kinky Boots dominated the awards, winning best musical as well as five other prizes.
Harris, who made his fourth appearance fronting the event, again drew plaudits for his hosting duties and show-stopping opening number.
"It took Neil Patrick Harris only about three minutes to banish any worries that the fearsome Host Fatigue Syndrome would overtake him and the Tony Awards on Sunday night," said the New York Times.
"He set the bar so high with his introductory flourish that fears of another familiar Tony malady haunted the rest of the CBS broadcast: the dreaded How Do We Top the Opening Number Disease."
The Los Angeles Times also praised the "invaluable, unshakeable" Harris.
The 39-year-old, its critic wrote, "was never too long out of view, and when he was around, he was put to good use".
The event also featured appearances from Tom Hanks, Jake Gyllenhaal, Scarlett Johansson, Sally Field and Mike Tyson.
Last year's Tonys was watched by six million viewers, down from the 6.9 million who saw the show in 2011.

Police say it was a suicide attack on a foreign military convoy which was travelling through the area.
A health ministry official said nine Afghans were among the dead.
A senior Nato official confirmed that three American contractors had been killed in the attack in the Macrorayan district.
No group has said it carried out the attack, although in recent months Kabul has been regularly targeted by the Taliban in a series of bombings.
The explosion took place not far from Kabul airport and the presidential palace. Witnesses said that children were among the injured and some foreigners were trapped in a destroyed vehicle.
An interior ministry spokesman quoted by the AP news agency said the blast destroyed more than a dozen civilian vehicles.
The bombing, close to a civilian hospital, is the latest in a series of recent deadly attacks following the announcement of a new Taliban leader.
Earlier this month, a Taliban suicide bomber attacked a checkpoint near the entrance to the international airport in Kabul, killing five people.
Before that, there were three deadly attacks in the city - on a police academy, a Nato base and an Afghan army base that killed at least 50 people.
The Taliban has stepped up its campaign of violence in recent months, taking advantage of the warmer weather of spring and summer. It has made some military gains, especially in northern Afghanistan.
This year's Tony Awards scored its best US TV ratings since 2009, with viewership up 20% from last year's show, according to the CBS network.
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An explosion has rocked the diplomatic area of the Afghan capital, Kabul, police have said, with at least 12 people killed and 60 injured.