The 38-year-old seamer took the first five wickets to reduce the visitors to 48-5, before Ben Cox (63) and George Rhodes (59) shared a stand of 94.
They were eventually all out for 230, losing their last four wickets for 30.
England Test captain Alastair Cook closed on 43, with Tom Westley 58 not out, as Essex reached stumps on 111-1.
Masters' seven-wicket haul added up to the second-best bowling figures of his career, bettered only by his 8-10 against Leicestershire at Southend in 2011.
Essex fast bowler David Masters told BBC Radio Essex:
"I'm getting a bit older now and can't play as many games, so when I am playing I'm generally fresh. They've looked after me well this year. I've played when they've needed me to play and hopefully I don't disappoint.
"My body takes a bit more of a battering now and it takes me a bit more time to recover. But I still love playing, I love bowling.
"It's quite a docile wicket actually. The shine came off the new-ball and it started to swing and I got the ball in the right areas. That can happen sometimes."
Worcestershire assistant coach Matt Mason told BBC Hereford & Worcester:
"We probably lacked a bit of application with the bat, particularly early on with some soft dismissals in there. And that last session was probably the poorest we have had as a bowling unit this year, so not an ideal day.
"When you win the toss and bat first you want to post 400, let's be honest. It looked a good surface and if we'd applied ourselves better you could bat and get some good partnerships.
"I wouldn't want to detract anything from Masters' spell. He did what he's done for his whole career - he put the ball on the spot and nagged away. He is very disciplined, but I don't think we were very good in defence."

Cathay is one of the world's biggest cargo airlines, and its decision is expected to have a sizeable impact.
Previously, the airline had said it would only transport shark fin that was sustainably sourced.
Shark fin is considered a delicacy in Chinese cuisine and is often served as a soup at upmarket banquets.
More than 70 million sharks are killed every year, according to WWF figures. Large numbers are exported to Hong Kong, where they are consumed or further exported to mainland China.
"On the issue of shark's fin, with immediate effect we are happy to agree to ban the carriage," Cathay Pacific said in a statement on Wednesday.
It said it had not approved any shark fin shipments over the last year, pointing out that it had turned down 15 shipment requests for shark-related products.
Early reports said the ban extended to all shark products on cargo and passenger flights, but the airline told the BBC it currently applied to shark fin only,
Cathay said it would continue to review its policy.
Marine conservationists hailed Cathay's decision, with one proclaiming that it would make Hong Kong "proud".
"More Hong Kong businesses need to follow the lead," Hong Kong-based conservationist Sharon Kwok told AFP.
Government data cited by the South China Morning Post shows that shark fin imports to Hong Kong dropped by 42% between 2010 and 2015 to 5,717 tonnes.
During this period there was also a significant decline in imports by air.
Cathay now joins airlines including British Airways, American Airlines, Qantas, Singapore Airlines and Emirates in banning shark fin.
David Masters took 7-52 to put Division Two leaders Essex in a strong position against Worcestershire on the opening day at Chelmsford.
[NEXT_CONCEPT]
Hong Kong-based airline Cathay Pacific has announced a ban on shipments of shark fin in a move that has been welcomed by conservationists.