Tomkins poached the only goal from a corner midway through the first half and manned an impeccable defensive effort at the John Smith's Stadium.
It meant Huddersfield had barely a sniff of an equaliser before Andros Townsend won a 68th-minute penalty and captain Luka Milivojevic converted his sixth spot kick of the season.
Roy Hodgson handed Mamadou Sakho and Wilfried Zaha their first starts since suffering respective calf and knee injuries last month and the extra quality they provided at either end of the pitch will serve Palace well during the crucial period to come.
Palace are up to 16th, a point and a place below Town and two above the drop line.
The match began amid a now customary din from Huddersfield's home support but there was a collective anxious gasp in the seventh minute when Milivojevic curled a free-kick fractionally wide.
Steve Mounie's touch let him down in the 12th minute, allowing Sakho to recover from his slack pass and make a last-ditch tackle on the Town striker, while Christian Benteke had an attempt blocked as both teams pursued the all-important breakthrough.
It fell to Palace in the 23rd minute after the marauding Zaha won a corner, Mounie and Jonathan Hogg failed to deal with the left-wing delivery and Tomkins prodded home at the second attempt.
Huddersfield roared back at their opponents, with Milivojevic making a timely intervention as Alex Pritchard stood poised to convert Collin Quaner's cutback.
Benteke, leading the line superbly for Palace, teed-up Townsend four minutes from the end of a frenetic first half but the winger shanked a shot wastefully over.
Chris Lowe's half-time introduction in place of full-back Scott Malone gave the hosts greater thrust down the left flank but clear openings remained scarce.
Tomkins thought he had a second after the hour when another Palace corner evaded the Huddersfield backline but, when the centre-back drove goalwards at the back post, Mounie was on hand to hack off the line.
Back in his natural habitat in the opposition penalty area, Mounie then lashed against the stanchion – an attempt that, for all their efforts, was Huddersfield's first shot of the match.
The state of the game offered increased opportunities for Palace to play to their strengths on the counter-attack and, when Mathias Jorgensen dived in on a rampaging Townsend, Milivojevic had the chance to seal the points from 12 yards.
He made no mistake, clattering his effort to Jonas Lossl's right as the goalkeeper guessed incorrectly.
Lossl twice saved impressively during the closing minutes from Yohan Cabaye - another of Palace's returnees - by which point Hodgson's great escape was firmly back on course.
Huddersfield have the spirit and organisation to survive too, on this evidence, but the lack of cutting edge in David Wagner's side - now scoreless in three - is a gnawing concern.
Key Opta Stats:
- Crystal Palace have won seven Premier League away points in 2018 (W2 D1 L3), one more than they picked up in their previous 12 away games in 2017 (W1 D3 L8).
- Huddersfield have failed to score in a league-high 17 different Premier League games this season. They have drawn a blank in eight of their last 11 games in the top-flight.
- Palace ended a seven-match winless run in the Premier League (D2 L5), securing their first victory since a 1-0 win over Burnley in January.
- Only Andrew Johnson (11) has scored more penalties in a single Premier League season for Crystal Palace than Luka Milivojevic (6).
- James Tomkins scored his first away goal in the Premier League since November 2016 versus Swansea.