Shai Hope held the key to the West Indies staying in the game but he received little in the way of support.
West Indies were 153 for six at lunch on Saturday's third day, a lead of just 82 runs in a series all square at 1-1.
Hope lasted just four balls after lunch, though, before Anderson found late movement down the slope to have him caught-behind and then doubled up by snaking through Devendra Bishoo's defences for a second-ball duck.
That left Anderson joint-second in that list alongside England fast-bowling great Fred Trueman, with ex-England all-rounder Ian Botham's eight five-wickets in innings hauls the most anyone has taken in Tests at "the home of cricket".
Play started in bright sunshine, a marked contrast to the grey skies that had encircled Lord's during the first two days.
England then took 28 overs to make light of a soft target in fine batting conditions, albeit in a low-scoring match, and claim the series 2-1 just before a slightly delayed tea.
Chase was out for his overnight three and West Indies were 94 for four.
Catches, or rather the lack of them, have beset England throughout the series and Ben Stokes was the guilty party as he dropped Jermaine Blackwood off Stuart Broad's bowling.
Anderson leads England to series victory over West Indies
Blackwood (5) perished not long after, though, clipping Anderson to Bairstow while playing away from his body, before Broad failed valiantly to take a return catch off Dowrich diving full stretch to his left.
James Anderson followed up taking his 500th Test wicket with career-best figures to skittle West Indies and guide England to a series victory at Lord's with a nine-wicket triumph.
Toby Roland Jones added to the two wickets he took on day two by removing Shane Dowrich for 14 and the West Indies reached the lunch break with a lead of 82, with the unsafe Shai Hope unbeaten on 60.
It was yet another significant contribution from the 23- year-old Barbados batsman, whose twin hundreds - including a maiden Test century - had provided the backbone of West Indies' series-levelling victory at Headingley.
Soon afterwards, he reached a richly deserved near three-and-a-half-hour 50 with a high-class back-foot punch wide of mid-on off Roland-Jones for his eighth four from 127 deliveries.
Hope, who also made a stylish 39 in hard conditions in the first innings at Lord's, then drove Roland-Jones past backward point for a third four in five balls.
Jason Holder had escaped a tough chance to Alastair Cook at slip off the last ball of the morning, when Root gave himself a sly over, but he could not make it count - mis-pulling Broad into the leg-side, where Anderson took the catch.