Broad’s haul of 6-31 in 14 overs saw the West Indies bundled out for 197 in reply to England’s first-innings 369 that featured his dashing 62.
England’s second-innings 226-2 declared saw opener Rory Burns make 90 as the West Indies were set a huge target of 399 for victory.
And there was still time for Broad to reduce the tourists to 10-2 at stumps on the third day.
Broad had the struggling John Campbell caught at first slip for a duck by England captain Joe Root and then moved to 499 Test wickets when nightwatchman Kemar Roach was caught behind.
Broad bowled the final over of the day’s play, with his last ball just missing Shai Hope’s outside edge.
The only bowlers with more than 600 Test wickets are a trio of former spinners - Sri Lanka’s Muttiah Muralitharan (800), Australian Shane Warne (708) and India’s Anil Kumble (619).
The only seamers ahead of Broad are his longtime England new-ball colleague James Anderson (589) and the retired pair of Australia’s Glenn McGrath (563) and the West Indies’ Courtney Walsh (519).
Broad took all the West Indies wickets to fall yesterday.
His burst of 4-14 in four overs ended the visitors’ first innings after they had avoided the follow-on and Broad had stumps figures of 2-8 in three overs.
England’s second innings saw Burns and Dom Sibley (56) share a stand of 114 - England’s first century opening partnership in a home Test since Alastair Cook and Alex Hales put on 126 against Pakistan at Edgbaston in 2016.
England captain Joe Root was 68 not out when he declared, amid concerns today’s play could be washed out.
No side has made more in the fourth innings to win an Old Trafford Test than England’s 294-4 against New Zealand in 2008.
Root declared when Burns, bidding for his third Test century, skied off-spinner Roston Chase to substitute wicketkeeper Joshua Da Silva.
Burns faced 163 balls including 10 fours.
Root had previously completed a 49-ball fifty when he drove Roach’s first ball back straight over the fast bowler’s head for four.
West Indies used three wicketkeepers yesterday after Shane Dowrich was hit in the face after a 90mph delivery from Shannon Gabriel burst through his gloves.
One-day international wicketkeeper Hope initially took over behind the stumps.
But match officials then allowed Da Silva, the back-up gloveman in the Test squad but not in the original XI for this match, to come on.
Burns, twice dismissed by Chase already this series, almost fell to him on 12 when beaten by a sharply turning delivery, only for the unlucky Da Silva to slip and miss the stumping chance.
West Indies resumed still needing 33 more runs to avoid the follow-on at 137-6.
They did that while Root delayed the entry of Broad into the attack.
But when he came on, the West Indies had no answer to him.
West Indies captain Jason Holder was lbw for 46 before Broad, controversially omitted from England’s first-Test loss at Southampton, had Roach caught by first slip Root for a duck and Rahkeem Cornwall lbw.
Broad ended the innings when Dowrich holed out for 37.