Chelsea blew a golden chance to close the gap on Manchester United who crashed to a 2-0 defeat against Fulham and Hiddink's side remain four points behind the leaders.
Hiddink had enjoyed a dream start to his career as Chelsea coach winning his opening four league games, but the Dutch coach could only watch in horror as Tottenham secured the three points at White Hart Lane.
Chelsea have amazingly yet to win a London derby this season, but Tottenham supporters will not care less as they saw their team all but secure their top-flight status and could even yet push for a European spot.
It could have been a different story if Chelsea had opened the scoring after just seven minutes when Michael Essien fired a blistering shot from the edge of the box which produced a fine save from Heurelho Gomes diving low to his right.
Tottenham slowly forced their way into the game and came close on 17 minutes following a long goal-kick from Gomes.
Chelsea defender Alex completely misjudged the ball and Robbie Keane fired a half-volley which was superbly saved by Petr Cech.
The home side threatened the Chelsea goal once again on 24 minutes. Vedran Corluka broke free into the Chelsea half before laying the ball across to Keane who struck his shot straight at Cech.
Gomes produced one of his best performances for Tottenham in their victory over Aston Villa last week and continued his impressive form when he made a fine save to deny Nicolas Anelka on 32 minutes.
Didier Drogba was forced to leave the field for Chelsea on the stroke of half-time following a challenge with Ledley King and Jonathan Woodgate, but was able to re-appear for the start of the second half.
Modric has been one of the star performers for Tottenham this season and he stole the headlines once again when he netted the all-important match-winner on 50 minutes.
Aaron Lennon weaved his way down the right-hand side and crossed in for the Croatian midfielder who showed all his class to fire a low shot past Cech into the corner of the net.
The home side should have doubled their lead on 57 minutes. Modric's corner fell to King who was completely unmarked inside the box but he flashed his header wide of the post.
Lennon turned provider once again just 60 seconds later picking out Modric but the Croatian midfielder directed his shot straight at Cech.
Chelsea threatened to snatch an equaliser, but Drogba smashed a low shot which was well-saved by Gomes on 67 minutes.
Frank Lampard's free-kick then picked out John Terry on 78 minutes but his close-range header produced a stunning one-handed save from Gomes diving low to his right.
Hiddink knew it was not going to Chelsea's day when Lampard's corner fell to Alex in stoppage time but he saw his header cannon back off the bar.