The Scotland international, 24, reached a century from just 70 deliveries and hit 18 boundaries and four sixes, as Sussex were all out for 345.
Sri Lankan spinner Sachithra Senanayake (2-79) led Worcestershire's fight back with two wickets in two balls.
Daryl Mitchell and Richard Oliver saw off the new ball to end the day without loss on 45.
Machan's fireworks came after Luke Wells was dismissed early, caught at third slip playing a loose shot to Chris Morris.
The number three attacked immediately, bringing up his half-century in 27 balls, before captain Ed Joyce (59) was dismissed by Jack Shantry (2-86).
Luke Wright continued his good form (51) but Sussex's lower order, with the exception of Ajmal Shahzad (45*), struggled once Machan was caught by Mitchell.
Senanayake picked up his first wicket for Worcestershire when he had Ashar Zaidi caught by Tom Fell, before trapping Steve Magoffin lbw next ball.
Sussex's tail struggled to push the team towards 400, with Gareth Andrew bowling well to dismiss Tymal Mills and Matthew Hobden cheaply.
Worcestershire had a scare shortly before stumps when opener Mitchell (18 not out) edged Shahzad to Joyce at second slip, but the Sussex captain was unable to cling on to the low chance.
Sussex batsman Matt Machan:
"I play better when I'm aggressive and go for my shots and it is something I have worked on.
"I'm trying to take my game forward in red-ball cricket by playing more positively.
"I only knew I was playing this morning so I decided to be aggressive from the start and once I'd got myself in I really enjoyed myself."
Worcestershire director of cricket Steve Rhodes:
"When a batsman hits the ball as sweetly as Matt did,  it can be difficult to bowl at.
"It was a special innings because he climbed into some really good balls. We were a bit shocked by the onslaught.
"I was pleased we managed to drag it back a bit after he chipped one up. It's a good cricket wicket. There is some pace there but you can score quickly."

The seven men had been given six-year jail sentences after an earthquake devastated the medieval town of L'Aquila in 2009, killing 309 people.
The verdict triggered alarm, with some saying that science itself had been put on trial.
On Monday an appeals court cleared the group of the manslaughter charges.
Judge Fabrizia Ida Francabandera ruled that there was no case to answer.
"The credibility of Italy's entire scientific community has been restored," said Stefano Gresta, the president of the National Institute of Geophysics and Volcanology.
The seven men - all leading scientists or disaster experts - had been members of a committee convened in L'Aquila in March 2009 following a series of tremors in the region.
Days after they met, a 6.3 magnitude quake struck the town in the middle of the night.
Many of L'Aquila's medieval buildings were destroyed, and some locals blamed the disaster committee for not providing adequate advice.
Prosecutors in the subsequent trial said the experts had offered falsely reassuring information to residents.
According to Reuters, they noted that one committee member had said there was "no danger" from the tremors.
Following the guilty verdicts, more than 5,000 scientists signed an open letter to Italian President Giorgio Napolitano in support of the experts.
Many argued that the convictions represented a fundamental misunderstanding of earthquake science.
Monday's decision to overturn the verdicts came after a month-long appeal process.
The prosecution can still seek to have the original verdicts reinstated via a higher court.
A career-best 135 from Matt Machan formed the backbone of Sussex's innings against Worcestershire at Hove.
[NEXT_CONCEPT]
A group of Italian scientists convicted of manslaughter for failing to predict a deadly earthquake have had the verdict quashed.