The West Indies were 109 for three in reply to England's first innings 258, a deficit of 149 runs, at lunch on the second day of the second Test in Leeds.
Brathwaite was 63 not out and Shai Hope 33 not out, with their unbroken partnership so far worth 74 runs.
Anderson removed both nightwatchman Devendra Bishoo and Kyle Hope in Saturday's first session on his way to brilliant lunch figures of three wickets for 10 runs in 12 overs, having dismissed Kieran Powell on Friday.
But they hit back when the swing specialist was given a rest by England captain Joe Root. The visitors resumed on their overnight 19 for one, having restricted England to under 300 with a much-improved bowling display following a humiliating innings and 209-run defeat in the inaugural day/night Test in Britain at Edgbaston last week that left them 1-0 down in the three-match series.
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Bishoo fell without adding to his overnight one when, to one of Anderson's worst deliveries, short and wide outside off stump, he edged an intended cut to wicket-keeper Jonny Bairstow.
And 31 for two became 35 for three when Anderson's full- length inswinger had Kyle Hope (three) outside-edging to second slip, where Root held a sharp catch diving to his left.
With the very next ball after Ali's appeal was overturned, Brathwaite drove him for six to complete an excellent 89-ball fifty that also featured six fours.