It was back-to-back draws for the Lions as the New Year encounter with Motherwell ends in stalemate.
Morgan Boyes’ header opened the scoring before Van Veen’s prompt reply.
Livingston captain Nicky Devlin had a retaken penalty saved by Liam Kelly at 0-0 after bundling home the rebound of the initial spot-kick.
Motherwell are now only above the play-off spot on goal difference.
“I don’t think we could have nicked something, I felt we thoroughly deserved to win,” said Motherwell boss Hammell.
“We created numerous chances, we should have scored more goals. It’s that end product [we’re lacking], we get into the areas we want”.
While Hammell’s men are winless in six, Livingston have gone five games without victory but rise a place to sixth.
Two wins in their last 14 league matches had increasingly brought Motherwell cause for concern, with their luck in dire need of turning.
Ricki Lamie cut a perplexed and dejected figure when referee David Munro pointed to the spot, judging the ball had struck the arm of the Motherwell defender, who was facing the other way. This was only the start of the drama.
Devlin’s initial penalty lacked vigour, allowing Kelly to push it back into the mix and gift the taker a second bite at success, which he put away.
However, a retake was ordered, seemingly for encroachment, and the Motherwell goalkeeper made no mistake in blitzing away any sniff of a rebound as Devlin again failed from 12 yards.
Injecting a well-needed wake-up call into the visitors, Van Veen began to exhibit what Hammell’s side have been missing in recent weeks as he forced Shamal George into action.
Epitomising an end-to-end encounter, Stephen Kelly crackled an effort just wide, before dropping a free-kick on to the head of Boyes at the back post for the Welshman to nod open his Livingston account.
Motherwell pounced back through a perfect piece of creativity as Van Veen’s razor-sharp instinct led to him looping a shot past George.
Level at the interval, an extended period of injury-time was played due to the head injury suffered by Cristian Montano, who didn’t return in the second half.
What did, though, was the tempo. His replacement, recent signing Steven Bradley from Hibernian, nearly made an immediate impact, catching Kelly off guard. Van Veen, at the crux of it again, crashed a close-range chance off the crossbar.
It swiftly became the clash of the Kellys, Stephen and Sean testing Liam’s goal with shots from range and a free-kick from the latter the last bid for a winner from either side as a draw petered out.
Match Report: Amy Canavan (BBC)
Livingston: George, Devlin©️, Obileye, Boyes, Montaño ▊ (Bradley 46) , St.Kelly, Shinnie, Sn.Kelly ▊, Bahamboula (Omeonga 59 ▊), Penrice, Anderson (Gonçalves 89)
Subs not used: Hamilton, Konovalov, Longridge, Cancar, Fitzwater
Goals: Boyes (39)
Motherwell: elly, McGinn, Solholm, Lamie, Penney, Goss ▊, Slattery ▊, Spittal, Cornelius, Shields (McKinstry 77), Van Veen
Subs not used: Oxborough, I’Donnell, Maguire, Blaney, Tierney, Spiers, Miller, Ross
Goals: Van Veen (42)
Referee: David Munro