With a day remaining in the 3,700km race, Rominger, the master of the mountains, achieved on the flat what he could not bring off in the Alps or the Pyrenees, and it lifted him from fourth position to second overall.
He covered the 48km from Bretigny-sur-Orge in 57min 02sec to beat the Basque whose only previous professional defeat in main time trials was by another Swiss, Alex Zulle, in the 1992 Tour of Catalonia.
Indurain was never ahead throughout the ride, and at two intermediate timings was third fastest, with Rominger and Poland's Zenon Jaskula faster.
Rominger's flat rear tyre added to the drama, and still he gave Indurain the biggest time-trial beating of his seven-year career. Indurain has twice lost short-distance time trials to the Italian Maurizio Fondriest and the Frenchman Thierry Marie.
Indurain was 1min 03sec slower 5.5km from the finish, but his finishing burst, which took him past the Colombian Alvaro Mejia, the overnight second-placed man, was not enough.
Despite defeat, Indurain increased his overall lead to 4min 59sec in readiness for the final leg into Paris, and, fingers crossed, a hat-trick of Tour victories.
Indurain's title as maestro of the time trial may have been dented but Chris Boardman is the man of the hour, and already the queue is forming to knock him from the pedestal.
Graeme Obree was six days on top of the world before the Olympic champion broke the 52km barrier on the Bordeaux velodrome. Hours later, he was side by side with the other maestro of beating the clock on the Tour podium.
Now Obree talks of another attempt, possibly in Stuttgart in September, and Rominger reckons that he personally is capable of better than Boardman.
'All I need is three months of preparation, and half a million Swiss francs,' the Swiss said. 'I know it is a lot to ask of a sponsor, but I believe I can make the record 53.200 kilometres.
'When Francesco Moser held the record I would not have dared to attack it, because he was my master. Now that has changed.'
His old team captain, now 42, is talking of trying again 10 years after setting his figure, which Boardman bettered by more than a kilometre. 'A lot has changed in equipment since my record,' the Italian, still an idol to many, said. 'I don't think we are talking of the same record now, and anyway Boardman has had a year of preparation whereas I had a season of racing in my legs when I broke the record.
'I still maintain that there should be records for outdoor and indoor, as in athletics.'
The Union Cycliste International eliminated such distinctions last year, and Moser's figures were set at altitude on an open-air track in Mexico.
Bernard Hinault, the five-times Tour winner, says Indurain is the one with a serious chance of improving Boardman's mark. 'The level is very high. Fifty kilometres was once the mark but now it could be 55, and I think he could reach that.'
Indurain is not committing himself, but Christian Pascaud, a technican at Corima, the makers of Boardman's latest monocoque bike, supports Hinault. 'Indurain has a greater chance to take the record even higher, and discourage a generation of contenders as Moser did in 1984,' he said.
TOUR DE FRANCE (Montlhery) 19th stage (48km time trial from Bretigny-sur-Orge): 1 T Rominger (Swit, Clas) 57min 02sec; 2 M Indurain (Sp, Banesto) 42sec behind; 3 Z Jaskula (Pol, GB-MG) +1min 48sec; 4 J Bruyneel (Bel, Once) +2:16; 5 G Bugno (It, Gatorade) +3:00; 6 J-F Bernard (Fr, Banesto) +3:05; 7 V Ekimov (Rus, Novemail) +3:09; 8 P Louviot (Fr, Once) +3:30; 9 C Chiappucci (It, Carrera) +3:41; 10 A Mejia (Col, Motorola) +3:43; 11 S Roche (Irl, Carrera) +3:58; 12 A Elli (It, Ariostea) +4:01; 13 G Faresin (It, ZG Mobili) +4:03; 14 L Desbiens (Fr, Castorama) +4:29; 15 R Conti (It, Ariostea) +4:31; 16 G Bortolami (It, Lampre) +4:33; 17 P Lance (Fr, GAN) +4:39; 18 R Alcala (Mex, WordPerfect) +4:47; 19 C Mottet (Fr, Novemail) +4:49; 20 G Perini (It, ZG Mobili) +4:50. Selected: 85 S Yates (GB, Motorola) +8:11; 101 R Millar (GB, TVM) +8:44.
Leading overall standings: 1 Indurain 90hr 29min 49sec; 2 Rominger 4min 59sec behind; 3 Jaskula +5:48; 4 Mejia +7:29; 5 B Riis (Den, Ariostea) +16:26; 6 Chiappucci +17:18; 7 Bruyneel +18:04; 8 A Hampsten (US, Motorola) +20:14; 9 P Delgado (Sp, Banesto) +23:57; 10 V Poulnikov (Ukr, Carrera) +25:29; 11 Faresin +29:05; 12 A Martin (Sp, Amaya) +29:51; 13 Roche +29:53; 14 Conti +30:05; 15 J-P Dojwa (Fr, Festina) +30:24; 16 O Rincon (Col, Amaya) +33:19; 17 Elli +33:29; 18 J Unzaga (Sp, Clas) +38:09; 19 R Virenque (Fr, Festina) +38:12; 20 Bugno +40:08. Selected: 24 Millar +44:20; 89 Yates +2hr 16min 38sec.
King of the Mountains: 1 Rominger 449pts; 2 Chiappucci 295; 3 Rincon 286.
Points classification: 1 D Abdoujaparov (Uzbek, Lampre) 263; 2 Indurain 136; 3 J Museeuw (Bel, GB-MG) 132.