The McLaren-Mercedes driver conducted a dignified rather than ecstatic champagne celebration in deference to the nation's emotions and then retreated to a private party in the team's compound.
Coulthard had endured an anxious summer, wondering if he might lose his job to Damon Hill. It affected his form, which in turn added fuel to the speculation. He arrived here, however, with a contract for next year and an abstracted view of his immediate objective. A lightning start and a pit stop to match carried him from sixth to his second win of the season and the third of his career.
Coulthard crossed the line 1.9sec ahead of Jean Alesi's Benetton-Renault. Heinz-Harald Frentzen in a Williams-Renault was third, and Jordan-Peugeot's Giancarlo Fisichella fourth.
The championship issue was reduced to a sideshow, Jacques Villeneuve's fifth place in the other Williams edging him a point closer to Michael Schumacher who, to the dismay of a record 115,000 crowd, could manage only sixth in the outclassed Ferrari. The gap between them is 10 points, with four races remaining.
This high-speed circuit suited the McLaren-Mercedes package and Coulthard, relieved of long-term concerns, sensed his chance as he sat on the grid. "I was so relaxed I almost knew I was going to win before the red lights went out. Pressure is a distraction. Pressure focuses the mind.
"You have highs and lows and this is a boost for everyone," he said. "I have never been afraid to admit my mistakes, but I have never doubted my ability."
Coulthard had not appeared on the rostrum since his triumphant opening to the season in Australia, hence his total of 24 points and fifth place in the drivers' standings.
The 26-year-old Scot was effectively half-way to a maximum haul here by the first corner, his characteristic acceleration and opportunism elevating him to third place.
There he stayed until midway through the race. Unable to pass Alesi, yet fairly secure in the knowledge he would not be outmanoeuvred by Frentzen. The new democracy in Formula One has opened the contest but done nothing to improve the prospects of overtaking.
The tedious procession reached the pit stops and a decisive flurry of activity. Coulthard followed Alesi down the lane and re-emerged ahead of the Frenchman. The efficiency of the McLaren crew had placed the race in their driver's control.
Coulthard said: "I always concentrate hard on the start because you can gain places in a few seconds that can take you 30 laps in the race. I was confident we would be quicker at the pit stop, because our car is better on fuel and our boys are the best."
He had survived his only moment of anxiety, catching the car as it slewed sideways. "I made a mistake and it could have put me off the circuit, but thankfully I was able to keep it on the road."
All that troubled him in the closing stages was how to conduct himself at the presentation ceremony. "I was wondering if I should spray the champagne," he said. "But I was told it would be acceptable to do so. It was fantastic to hear the national anthem. It was very emotional."
Schumacher who had struggled all weekend for a better response from his car, is content to be heading for Austria with limited damage to his championship cause. He admitted: "It could have been a lot worse."
That was the sentiment of Johnny Herbert and his Sauber-Petronas camp after the Englishman was put out of the race in an incident involving Schumacher's younger brother, Ralf. The German's Jordan appeared to squeeze Herbert into no-man's land and the Sauber careered into a tyre barrier at 150mph.
Herbert said: "What he doesn't seem to understand is that in very high- speed places like that you need to give the other guy racing room. I don't mind a battle or a bit of racing, but what he did is not the way to do it. It was dangerous. It was unnecessary and unacceptable, and the sign of an inexperienced driver who has a lot to learn about the art of racing closely at high speeds."
His boss, Peter Sauber, added: "Race drivers who look for an advantage in this way not only endanger the health of other drivers, but also do the image of our sport no favours at all."
Schumacher, however, replied: "I thought I had passed Johnny and that he had enough room, but during the braking I felt him touch my right rear wheel. I felt the car jump forward and at first I thought it was a bump, but then I saw Johnny spin off, so I realised he had hit me."
Eddie Irvine, in the other Ferrari, finished eighth, while Hill retired his Arrows-Yamaha with a blown engine.
1 David Coulthard (GB) 10pts
(McLaren-Mercedes) 1hr 17min 04.609sec
(average speed 147.885mph/238.036kph)
2 Jean Alesi (Fr) 6pts
3 Heinz-Harald Frentzen (Ger) 4pts
4 Giancarlo Fisichella (It) 3pts
5 Jacques Villeneuve (Can) 2pts
6 Michael Schumacher (Ger) 1pt
7 G Berger (Aut) Benetton-Renault +12.471; 8 E Irvine (GB) Ferrari +17.639; 9 M Hakkinen (Fin) McLaren-Mercedes +49.373; 10 J Trulli (It) Prost-Mugen- Honda +1min 02.706sec; 11 S Nakano (Japan) Prost- Mugen-Honda +1:03.327; 12 G Morbidelli (It) Sauber +1 lap; 13 R Barrichello (Br) Stewart-Ford +1 lap; 14 T Marques (Br) Minardi-Hart +3 laps.
Not classified (did not finish): 15 D Hill (GB) Arrows-Yamaha 46 laps completed; 16 R Schumacher (Ger) Jordan-Peugeot 39; 17 J Herbert (GB) Sauber-Petronas 38; 18 M Salo (Fin) Tyrrell-Ford 33; 19 J Magnussen (Den) Stewart-Ford 31; 20 J Verstappen (Neth) Tyrrell-Ford 12; 21 U Katayama (Japan) Minardi-Hart 8; 22 P Diniz (Br) Arrows- Yamaha 4.
Fastest lap: Hakkinen 1min 24.808sec.
1 Ferrari 85pts
2 Williams 84
3 Benetton 53
4 McLaren 38
5 Jordan 28
6 Prost 20
7 Sauber 15
8 Arrows 7
9 Stewart 6
10 Tyrrell 2
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