Darnell McIntosh scored two tries as Huddersfield came from behind to earn a draw.
The Giants are without a win in six Super League matches but at least avoided a third straight defeat after full-back McIntosh inspired a second-half comeback.
The Giants lost second-rower Dale Ferguson to a head injury and it soon got worse for Rick Stone’s side as Saints took their first chance to put points on the board.
Mark Percival made the initial break and Zeb Taia kept his composure at dummy-half to pop the ball up for Theo Fages to hit at speed and finish.
Offloads from Percival and Taia put Fages into space and the France international half-back left McIntosh on the floor with a big right-foot step to race clear for his second try.
Ferguson returned for Huddersfield but there was nothing he could do to prevent Swift from making it three in 12 minutes.
Huddersfield gave themselves hope of a comeback just after the hour mark.
Brough had been quiet on his return from suspension but it was his pass that set former Saints half-back Lee Gaskell free and gave the Giants the field position for McIntosh to crash over.
Huddersfield were sensing an unlikely victory after McIntosh took advantage of Fages’ fumble in the in-goal area from Brough’s kick to touch down. Brough converted to pull the Giants to within four points and it was his kick that allowed Wood to finish.
St Helens: Lomax, Makinson, Morgan, Percival, Swift, Fages, Smith, Walmsley, Lee, Douglas, Taia, McCarthy-Scarsbrook, Wilkin. Substitutes: Amor, Walker, Peyroux, Knowles.
Huddersfield Giants: McIntosh, McGillvary, S. Wood, Mellor, Murphy, Brough, Gaskell, Ikahihifo, Hinchcliffe, Wakeman, Roberts, Ferguson, Clough. Substitutes: Rapira, Leeming, Mason, Dickinson.
Referee: Chris Campbell (RFL)