And the jihadist group carried out a double car bomb attack that killed 11 people in northwestern Hasakeh city, where regime forces have been fighting to fend off an IS assault.
Syrian state television and Hezbollah's Al-Manar station announced the advance into Zabadani on Sunday, a day after a major operation against it began.
"Heroic army forces in cooperation with the Lebanese resistance took control of the Al-Jamaiyat neighbourhood in western Zabadani and the Al-Sultana neighbourhood in the east of the city," state television said.
"Operations are continuing with dozens of terrorists killed and wounded."
The Syrian Observatory for Human Rights said regime forces and Hezbollah had entered Zabadani and intense clashes were underway in its east and west.
Army helicopters dropped at least 22 barrel bombs on the town and were also shelling it heavily, said the Britain-based monitoring group.
At least 14 pro-government and Hezbollah fighters had been killed in the past 24 hours, along with at least 12 rebels and a civilian, it added.
The official SANA news agency said it had killed "dozens of terrorists," a term the regime uses to describe its armed opponents.
- Last rebel border bastion -
Zabadani was one of the first towns to fall into rebel hands, in early 2012, and is now the opposition's only remaining stronghold along the Lebanese border.
The town is strategically important for the regime in part because of its proximity to the capital and the highway that runs from Damascus to Beirut.
Zabadani has been under siege for more than a year, and most of the civilians have already fled, according to activists.
Alwan, an activist from Zabadani who now lives outside Syria, said there were still thousands of civilians in the east of the town and many wounded people.
"I don't know what their fate will be," he told AFP.
The town is in the Qalamun region, once an opposition stronghold but mostly recaptured by the regime and Hezbollah in a campaign between late 2013 and April 2014.
Elsewhere in Syria, the US-led coalition said it carried out 18 air strikes against IS's de facto Syrian capital of Raqa, destroying vehicles and bridges.
The Observatory said the raids killed at least 30 people, among them six civilians including a child.
The US-led coalition said the strikes were some of its heaviest since it began bombing the IS in Syria in September last year.
"The coalition conducted multiple air strikes in northern Syria to deny Daesh's freedom to manoeuvre," coalition chief of staff Brigadier General Kevin Killea said in a statement.
"These strikes provide the forces on the ground the opportunity to act decisively against Daesh."
- IS bombs kill 11 -
The raids came after IS released a video Saturday showing boys and teenagers killing 25 Syrian soldiers in the ancient amphitheatre in the city of Palmyra.
The execution-style murders had been reported earlier, in the days after IS seized the city from government forces on May 21, but the video was the first evidence of the killings.
Palmyra's ancient ruins are listed as a UNESCO World Heritage Site and there has been concern IS might seek to destroy its heritage, as it has done elsewhere in Syria and Iraq.
In northwestern Syria, the Observatory said at least 11 regime forces were killed in a double car bomb attack on a checkpoint in the city of Hasakeh.
State television had reported the attack, saying it was near a power station but giving no toll.
IS launched a new assault against Hasakeh last month, seizing control of two districts from government forces, which share security responsibility in the city with Kurdish fighters.
The jihadists have been forced back in some areas, but fighting has continued.
More than 230,000 people have been killed in Syria since anti-government protests erupted in March 2011, precipitating a civil war pitting pro-regime forces, rebels and jihadist groups against each other.
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