Up 16-14 with 20 seconds to play in a high-quality grand-final rematch on Thursday, Parramatta gave the Panthers one last chance to equalise when co-captain Junior Paulo struck Zac Hosking around the chin and found himself sin-binned.
Nathan Cleary kicked for touch and once the ball was in play, drilled a two-point field goal to tie the game as the siren sounded.
But Mitch Kenny's high shot on Waqa Blake reduced the visitors to 12 in the first minute of extra time and marched the Eels upfield where Moses sealed the result.
"I definitely don't think it was a sin bin, a penalty maybe," Panthers coach Ivan Cleary said of Kenny's hit.
"He was just getting off the line like he always does trying to make a play.
"There were a couple of big penalties in big moments tonight. It's a shame."
The win at CommBank Stadium will give the Eels untold confidence following a 0-3 start that threatened to bring their premiership tilt unstuck before it had begun.
Eels coach Brad Arthur said the win needed to inspire the Eels into form.
"We'll see how we respond to it next week," he said.
"We've had some tough games (to start the year) and we could've won all three of them. We've been victims of our own circumstances.
"At least tonight we took control of it. If we got beaten tonight, there wasn't much more we could've done footy-wise to try and win it."
Penrith, meanwhile, have begun their premiership defence with two losses from their first three games.
Their attack has been below their grand final-winning best, producing only 44 points across the first three games compared to 86 in the same period last year.
"Disappointing to have the loss but I think we'll get a lot out of that game," coach Cleary said.
Hours after signing his highly-anticipated contract extension, Moses had some great moments in regulation time, including two forced dropouts in quick succession, a one-on-one tackle on Luke Garner close to the line and a hit on Jarome Luai that forced an error in the first half.
Ryan Matterson was solid with 166 run metres on his return from the three-match suspension he chose over a $4,000 fine after the grand final.
The Eels controlled the territory battle early, completing at 94 per cent across the first half, and drew first blood when Dylan Brown split the defence with a grubber kick for Bryce Cartwright.
But the Panthers scored next against the run of play - Isaah Yeo broke his arms free from the defence and offloaded to Scott Sorensen, who found the omnipresent Dylan Edwards.
A Nathan Cleary penalty goal levelled the scores 8-8 on the halftime siren.
On NRL debut, 23-year-old Penrith junior Brendan Hands broke the stalemate for Parramatta, before Hosking, called in as an injury replacement for Liam Martin, brought the Panthers back within two.
The game's best clutch player, Cleary had the game back on level terms in the dying seconds but was trumped in extra time by fellow No.7 Moses.
The Panthers will lose bench hooker Soni Luke for next week's game after he failed his HIA in the second half.
