The stalwart seamer's 62 from 45 deliveries included the third fastest fifty by an Englishman - from 33 balls - as the home side recovered from 280 for 8 to reach 369.
Meanwhile, West Indies coach Phil Simmons admitted his side had struggled to keep the old firm of Broad and Jimmy Anderson at bay as they face the prospect of handing over the Wisden Trophy before it is replaced by the Richards-Botham Trophy.
In a partnership of 76 for the ninth wicket, Broad thrashed nine fours and one high-and-mighty six over midwicket.
And at stumps, the West Indies had slumped to 137-6, a deficit of 232 runs, to give England the edge in the deciding match of a three-Test series now all square at 1-1.
Broad, who was omitted from the first Test of the series, took 6-31 in the morning to wrap up the West Indies' first innings. "It was one of those situations where you take it to the bowling attack, and it suited my style".
"I'll work hard to get there and we'll see how many I can go past 300", added Roach, now in his 59th Test following a debut in 2009.
"It does feel like a little bit of weight off my shoulders", Pope said.
Richards reserved many of his best performances for England, including a majestic 291 at The Oval in 1976 and a blistering unbeaten century in West Indies' World Cup final win at Lord's three years later. They came out after lunch under gray, threatening skies at Old Trafford, disgusting conditions to face one of the strongest and deepest pace attacks England has put out.
"It's a pretty ridiculous achievement to get 500", said Rory Burns, who scored 90 in England's second innings.
And there was time before tea for James Anderson to strike on his Lancashire home ground when a superb delivery from England's all-time leading Test wicket-taker had Shai Hope caught behind.
Archer, supposedly the new star of England, was first change and worked in the shadows.
"What he has done in Test cricket, in one-day cricket, in T20 cricket, I don't think so there's anyone, let alone in India, there isn't anyone who's even close to him in world cricket at the moment", he was quoted as saying in Star Sports show "Cricket Connected".
The Windies, who won the first test in Southampton before losing the second match in Manchester, are looking to capture a test series in England for the first time since 1988.