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The Portuguese attacker came close again 10 minutes later when he combined with Ryan Mendes on the right before firing an effort wide of the near post.
Leeds began to put the Forest defence under more pressure after the half-hour mark and had a chance to get the equaliser when Charlie Taylor's cross was met by Chris Wood, but the striker could not keep his header down.
Wood had another sight of goal 10 minutes after the restart when he was released in the Forest half, but he took the shot on first time and sent it well off target.
Chances continued to arrive at both ends of the field, and Forest were indebted to Dorus de Vries just before the hour mark as he kept out a Stuart Dallas header following Scott Wootton's ball into the box.
It was Silvestri's turn to be tested with 15 minutes remaining, as the Italian pulled off a fine diving stop to keep out Jamie Ward's long-range drive before the Leeds defence completed the clearance.
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It was Leeds who got the crucial second goal of the game with only 10 minutes remaining, however, as Sam Byram made it three goals in as many games by nestling an effort into the bottom corner.
Both sides went in search of a winner in the closing stages, with Leeds going close through Wood and Mirco Antenucci, and Forest threatening again from a curling Ward effort.
It was the hosts who went closest to grabbing a winner when a blocked Ward effort fell to Oliver Burke, only for the striker to see his attempt come back off the post in the final minute of normal time.
Leeds continued to push until the final seconds, with Luke Murphy coming closest for the visitors, but ultimately both sides were forced to share the points in a match that saw Forest extend their unbeaten streak to six games, while Leeds are now without a loss in five.