Leeds scored with their first attack of the game, with Nick Barmby's lofted ball finding Harry Kewell on the left. Viduka broke through the middle ahead of Titus Bramble as the Australian crossed for his countryman to open the scoring in the fourth minute.
United's first real effort came in the 16th minute, when Alan Shearer chested Nolberto Solano's header down before shooting low at Robinson. Woodgate then went close for Leeds before referee Gallagher waved away a penalty appeal at the other end after Danny Mills appeared to handle the ball in the box.
Both Danny Mills and Smith were booked for fouls on Olivier Bernard as United came into the game and Laurent Robert tested Robinson in the 33rd minute with a low drive.
Shola Ameobi and Bernard then had chances but again Robinson was equal to them.
He didn't get a proper contact on his low shot but it still took a fine save to deny the Magpies an equaliser.
Newcastle started the second half as they finished the first, with Bernard flashing a low shot just wide of the post in the 50th minute, just after Gary Speed had been booked for a foul on Viduka.
Shearer and Ameobi then wasted chances as United continued to pressure Leeds before Kewell shot wide for the Whites.
Sir Bobby Robson then brought Hugo Viana on for Speed and Craig Bellamy for Ameobi.
But it was Leeds who had the next chance, with Shay Given making a double save from Kewell and Viduka. At the other end Robinson tipped a long-range effort from Solano over the bar.
Andy Griffin replaced Andy O'Brien late in the game, being booked almost straight away for a foul on Barmby, before Eirik Bakke came on for Viduka in the 85th minute.
Two minutes later Smith struck with a first-time effort after Bramble's clearance fell to his feet.
Bramble was booked in the 90th minute for a foul on Lee Bowyer.
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