The West Indies were 151-5 in their second innings at lunch on the third day, with Hodge 52 not out after opener Mikyle Louis had made his maiden Test fifty earlier in the day.
But that left the West Indies just 57 runs ahead, with England already 2-0 up in a three-match series.
West Indies resumed on 33-2, still 61 runs behind an England first-innings 376, where Jamie Smith fell agonisinly short of a maiden Test century in making 95 while further fifties from Joe Root (87), Chris Woakes (62) and skipper Ben Stokes (54) helped the hosts recover from a collapse to 54-5.
Louis, 18 not out overnight after being dropped on nine by Stokes, and Alick Athanaze (five not out) walked out beneath a sunny blue sky, with a placid pitch also offering the prospect of good batting conditions.
Off-spinner Shoaib Bashir and express quick Mark Wood opened the bowling after the pair had teamed up to good effect during England's 241-run win in the second Test at Trent Bridge.
Wood almost had Athanaze out for seven when a flashing drive flew through Harry Brook's hands at third slip.
But the left-hander's reprieve was short-lived, with Athanaze lbw for 12 to the 20-year-old Bashir -- who took 5-41 in the second innings at Trent Bridge -- after missing a sweep.
Nevertheless, the West Indies were 96-3 at drinks, having avoided the embarrassment of a second innings defeat in three Tests following an innings and 114-run loss in the series opener at Lord's.
Louis, who only made his debut in that match, completed a maiden Test fifty in style when he slog-swept Bashir for six to reach the landmark in 85 balls, also including four fours.
And the 23-year-old cleared the ropes again when he drove Bashir over long-off for another six.
Louis, however, fell soon afterwards when paceman Stokes drew him into edging a full-length ball to Zak Crawley at second slip.
It was the end of a stand of 72, with Louis out of 57.
Hodge, who made his maiden Test century at Trent Bridge, went to fifty in just 56 balls, including seven fours.
But new batsman Jason Holder was dropped by Crawley in the slips on 12 only to be dismissed for that same score when lbw to a full-length delivery from fast bowler Gus Atkinson.
