Richard Cockerill got the better of former boss at Leicester Tigers Dean Richards, Edinburgh's bonus-point win meant they went top of their Heineken Champions Cup pool.
With Scotland cap Jon Welsh, Craig Mitchell and Paul Mullen all also unavailable, loosehead Sami Mavinga was on the bench but it raised the prospect of Newcastle having to play with 14 men and face uncontested scrums in the event of any further setbacks.
"It was a night for the underdog, but they took a similar team to Tolulon and got a result, so it was a good five points - but we won't get carried away". Van der Walt's conversion attempt flicked the post but went the right side for Edinburgh fans.
"They've got three fit props, they're all loosehead props".
You can only beat the team which appears in front of you, and Edinburgh head coach Cockerill was satisfied with what his players had achieved - although he was not entirely enthused by the performance. There was a nervous moment for Edinburgh when Newcastle flier Radwan raced into space, replacement hooker Dave Cherry saving the day with a vital cover tackle to preserve the two score cushion.
The Falcons wanted to register 24-year-old Jack Payne but as this had to be done before midday on Tuesday, they were denied by EPCR.
After a scrappy start, Edinburgh fell behind to a fourth minute penalty from Falcons stand-off Brett Connon after a Pierre Schoeman offside at a ruck, but they recovered their composure and after building pressure through several tight phases, the hosts took the lead when Hamish Watson blasted over from close range.
When Edinburgh did eventually try to drive their scrum, it brought a penalty and although van de Walt hit the upright again, he was on target when Darcy Graham retrieved possession and Newcastle were penalised again.
The visitors worked the hands really well, finding Radwan who stayed in play and bounded down the left wing before diving over for the go-ahead try. The parity would not survive to the break though as Connon knocked over another penalty to give the English side a 13-10 half-time lead.
And the next time they got down in the Falcons 22 the home side turned the screw with a succession of penalties and scrums inevitably leading to a penalty try with 55 minutes played.
Newcastle went until just before the interval, when Connon again slotted over after a Edinburgh infringement.
The decision had, though, seemed indicative of their mindset, this match representing a chance to secure a four try bonus point win even in treacherous conditions and they registered their first a quarter of an hour into proceedings when they earned another chance to set up a lineout drive in their opponents' 22 and this time got it right.
Edinburgh: B Kinghorn; D Graham, J Johnstone, C Dean, D van der Merwe; J van der Walt, H Pyrgos; P Schoeman, S McInally (capt), WP Nel; B Toolis, G Gilchrist; J Ritchie, H Watson, V Mata.
Newcastle: A Tait; T Arscott, C Harris, P Bettencourt, A Radwan; B Connon, T Takulua; A Brocklebank, G McGuigan, S Lockwood; T Cavubati, G Young; R Burrows (capt), G Graham, C Chick.