Like Wales did, they trailed 15-3 at the break, but it was Welshman Dafydd James who rescued them with an opportunist try in the 64th minute.
Quins skipper Andre Vos was also an inspiration, tackling his heart out and setting up a 44th minute try by left wing Ugo Monye.
Bath's trials and tribulations – they are currently missing 23 first-team players through injury or illness – continued right up to kick-off.
Alex Crockett bravely declared himself available for selection despite a hernia but Bath spared him further pain by getting Ryan Davis released from England Under 21 duty in time to take his place.
Then, incredibly, Matt Perry pulled out after straining a muscle in a warm-up, forcing a reshuffle which saw Joe Maddock switch to full back and new signing Steve Booth made his debut on the wing.
Jeremy Staunton put the visitors in the lead after 28 minutes, but Bath's old head Rob Fidler celebrated his 150th Zurich Premiership appearance by galloping 15 metres for a rare try five minutes later.
Chris Malone converted to give Bath a 7-3 lead.
Bath took advantage of an embarrassing mix-up between Ugo Monye and Tom Williams which left Williams needing attention after a sickening collision. Malone kicked the resulting penalty to make it 10-3.
The home side were well in control at this stage and hooker Lee Mears burst through the Quins defensive line to score in first half injury time.
Monye's try four minutes into the second half, converted by Staunton, wrested the initiative however and Quins spent most of the second half on the attack.
Bath's difficulties escaping from their own half were compounded by Maddock's big kick straight into James' arms on 63 minutes, leaving the former British Lions centre with a simple run to the line.
For Bath:Tries: Fidler, MearsCon: MalonePen: Malone
For Quins:Tries: Monye, JamesCons: Staunton 2Pen: Staunton
Bath: 15 Matt Perry, 14 Joe Maddock, 13 Andrew Higgins, 12 Alex Crockett, 11 Andy Williams, 10 Chris Malone, 9 Martyn Wood, 8 Zak Feaunati, 7 James Scaysbrook, 6 Geraint Lewis, 5 Rob Fidler, 4 James Hudson, 3 Chris Loader, 2 Lee Mears, 1 Heinrich Kok Replacements: 16 David Ward, 17 David Flatman, 18 Gareth Delve, 19 Ramiro Pez, 20 Hugh Perrett, 21 Nick walshe, 22 Steve Booth
NEC Harlequins: 15 Tom Williams, 14 George Harder, 13 Dafydd James, 12 Mel Deane, 11 Ugo Monye, 10 Jeremy Staunton, 9 Steve So’oialo, 8 Tony Diprose, 7 Andre Vos (c), 6 Nick Easter, 5 Simon Maling, 4 Jim Evans, 3 Ceri Jones, 2 Tani Fuga, 1 Mike Worsley Replacements: James Hayter, Jon Dawson, Simon Miall, Roy Winters, Luke Sherriff, Dave von Hoesslin, Arwel Thomas, Simon Keogh
Referee: Steve LanderTouch judges: Huw Jones-Williams, Paul Emerson