Visser's scoring touch was missed by the capital side during his long injury absence last season, but he showed that his opportunist instincts had survived the leg fracture that robbed Edinburgh of his services from November onwards.
Overall, Edinburgh's performance was a little shaky in places, but their lapses could probably be forgiven in a match in which they called on a dozen replacements. In fairness, they also held their defensive shape superbly well towards the end, when Newcastle were pushing desperately to close the gap on the scoreboard.
Sticking with the tactics they had used against Leicester at the Greenyards last weekend, Edinburgh treated the game as a serious contest rather than an exhibition match, and they were committed and abrasive in contact right from the off. The same pragmatism informed Greig Tonks' decision to take a pot at goal with their first penalty chance, after seven minutes, although the fly-half stroked that effort just wide.
It was his opposite number, the impressive Argentinian playmaker Juan Pablo Socino, who finally got the scoreboard moving, clipping over a straightforward penalty with 15 minutes on the clock. However, that score was unquestionably against the run of early play, and Edinburgh at last got some reward for their ambition when Visser, the former Falcon, raced after a grubber kick by Tonks, hacked the ball over the line and got his hand to it for the first try.
The delight of Visser, who had been a peripheral figure at Newcastle towards the end of his time with the north-east club, was obvious. But scoring against your former employers was soon to become the theme of the evening as Newcastle responded with a try by Mike Blair, who scuttled over in the 26th minute after the Falcons had caught Edinburgh on the hop with a quickly-taken penalty.
Edinburgh's flashes of ingenuity came more rarely, although there were a couple of excellent charges by Jack Cuthbert from full-back. Tonks, who missed the last four months of last season with a shoulder injury sustained on Scotland A duty, looked reassuringly solid in the No.10 berth, but it was his half-back partner, Sam Hidalgo-Clyne, who produced the best individual moment of the first half when he latched on to a loose ball, scuttled past a posse of defenders and was only brought down by the last defender.
Socino's conversion of the Blair try had nudged the Falcons into a 10-5 lead. However, by half-time it had been overhauled, with two penalties by Tonks putting Edinburgh's noses just in front, 11-10 at the break. The advantage probably flattered the Scots just a little, but Newcastle could have no serious grievance about the scoreline after such a closely fought opening period.
The impressive displays of Cuthbert and Hidalgo-Clyne suggested their removal at half-time - replaced by Nick McLennan and Sean Kennedy - was more about protecting them for next weekend's Guinness PRO12 opener against Munster than anything else.
Newcastle also made a raft of changes, but they spent most of the third quarter on the back foot as Edinburgh gnawed away chunks of territory. For the most part, the English side coped well enough, but they were left exposed when Edinburgh took a quick lineout on the left side with 55 minutes played.
The ball was collected by Visser, and the strapping winger punished his old colleagues once again with a ferocious burst of pace, scything through the defence on a blistering diagonal run that ended with a touchdown between the posts.
The try had an energising effect on Newcastle as they fought desperately to get a new foothold in the game over the next 10 minutes. The Edinburgh defence held firm, but their resolve finally broke when Newcastle won a lineout in the right corner, drove the resultant maul forward and sent Scott Wilson over for their second try.
That cut Newcastle's deficit to just three points, and after another wave of substitutions they began to look much the stronger side. Edinburgh were stretched close to breaking point as wave after wave of Newcastle attacks poured into their 22, and they would surely had taken more damage on the scoreboard had the Falcons shown a touch more composure in possession.
Instead, Edinburgh managed to clear their lines with a couple of relieving kicks, and one of their breakouts led to a penalty just inside the Newcastle half. By this stage, Tom Heathcote had taken over from Tonks as fly-half and goalkicker, and the former Bath player kicked a mighty goal to stretch Edinburgh's lead to 21-15.