The 33-year-old Abdoujaparov, whose eight previous wins in the Tour had come from sprint finishes, broke away from a group of five riders in the final climb of the day's 186.5-km ride from Besse.
``My team is not strong enough to prepare sprints for me so I have to look for other ways,'' said Abdoujaparov, who crossed the line seven seconds ahead of Italian Mirco Gualdi with Frenchman Laurent Madouas a further two seconds back.
Riis stayed safely within the pack, which came in nearly five minutes later, to retain his overall lead of 56 seconds over Abraham Olano of Spain with Russian Evgeny Berzin third a further 12 seconds back.
``I feel stronger every day and I'm confident I can reach my goal which is to win the race,'' said the 32-year-old Dane, who attacked from the start.
He reached the summit of the day's main climb, the Croix-Morand pass, in second position behind Frenchman Richard Virenque. With help from his team mates in the Telekom stable, Riis caught the leader in the descent and opened a break of nearly 40 seconds on the likes of Spaniard Miguel Indurain and Switzerland's Tony Rominger.
Indurain and Rominger fought back to catch the lead group as 19 riders, all way back in the overall standings, tried their luck at the front.
Five times Tour winner Indurain, still a poor eighth overall and over four minutes behind Riis, was expected to attack to keep his chances of a record sixth title alive. ``I was surprised to see him fall back,'' said Riis. ``I thought he would try something but perhaps he just couldn't.''
Riis has little to fear from Monday's relatively undemanding 176-km 15th stage from Brive to Villeneuve-sur-Lot.
Abdoujaparov promised he would press for a repeat performance. ``The finish is fairly flat and if there's a mass sprint, I'll go for it,'' said the sprinter from Tashkent.
Indurain said he was now looking forward to three stages in the Pyrenees from Tuesday to gain some time. ``It will be tough but I haven't lost yet,'' he warned. ``It will be difficult because the men in front are strong but hopefully, I'll be able to attack at the right time.''
Asked if he feared Riis, he said: ``No. I respect him but I'm not afraid of him.''
The 33-year-old, whose previous eight Tour stage victories had come from sprint finishes, crossed the line first after escaping from a group of five front-runners just before the final climb in the day's 186.5-km ride from Besse.
``My team is not strong enough to prepare sprints for me so I have to look for other ways,'' said Abdoujaparov, after his victory in the 14th stage.
``I'm still a sprinter, I'm not afraid.''
Once in a class of his own when it came to sprinting in the last few hundred metres, Abdoujaparov has been outclassed this year by a new generation of specialists including Italian Mario Cipollini and German Erik Zabel.
But the man who won the Tour's green jersey as points classification winner three times is still hungry for victory.
He has led breakaway groups several times since the race started last month from the Dutch city of Den Bosch.
Often criticised in the past for his reckless finishing, Abdoujaparov, now with the small Italian stable Refin, showed on Sunday that he could also win without controversy.
``I knew I had to get away before the start of the climb because I'm not exactly a mountain specialist,'' said Abdoujaparov, from Tashkent. ``I wanted this win badly and it's good for the team too. I'm delighted.''
He promised the Abdoujaparov of old would be back to his best over the next few days and possibly as soon as Monday in the 15th stage to Villeneuve-sur-Lot.
``The finish is fairly flat and if there's a sprint, I'll go for it,'' he said.
But there is another stage he has in mind and that is the very last one on the Champs-Elysees on July 21.
He has claimed it twice, in 1993 and again last year, but it is also the scene of one of his worst Tour moments. In 1991 he crashed into the barriers with victory in sight, sustaining severe injuries.
``It's in a week and I'm feeling better and better so maybe I can win it again,'' he said.
Long regarded as merely a useful team mate, the powerful Riis, who was 56 seconds ahead of second-placed Abraham Olano of Spain after Sunday's 14th stage, said he really thought he could win the race. ``I feel very strong and I'm really confident,'' he said. ``The race is not over yet and many things can still happen but I believe I can win.''
Riis, fifth overall in 1993 and third last year, showed his strength in the first few miles of Sunday's ride.
He reached the summit of the day's first challenge, the Croix-Morand pass, in second position just behind Frenchman Richard Virenque.
Then, with substantial help from his Telekom team mates, he took his place in a leading group while several contenders, including Indurain, briefly dropped back. ``I was surprised to see Indurain fall back,'' he said. ``I thought he would try something but perhaps he just couldn't.
Indurain, who undermined his chances of a record sixth win with a rare off-day in the Alps, lies a modest eighth overall over four minutes behind the leader. ``I don't kow what's wrong with him,'' said Riis. ``You just ask him. All I know is I'm feeling fine.''
If he rides in front from time to time just to show how strong he is, Riis, using the same policy as Indurain the previous years, does not make unnecessary efforts and allows harmless riders to try their luck.
``My goal is to win the race and I can't afford to lose any energy,'' he said.
Indurain has said exactly the same thing many times.