Dolan hit a 97 average with 69 percent on the doubles the real difference for 'The History Maker' as he set up a tie with Gary Anderson next up.
Kumar played well on his second time at the Alexandra Palace showing a rise in standard for the Indian Qualifier but it still wasn't enough to displace Dolan.
Both players played well to begin the first set with Kumar missing a dart for the set and Dolan as a result punished with double 16 in the decider to take the lead and the early initiative from the Indian qualifier.
Dolan produced a brilliant 100 checkout to lead the second set and the Northern Irishman took the second set 3-1 to double his lead with a 96.3 average and 55 percent on the doubles as he looked good up to this point.
He was up at 8/14 in the requisite set as he edged towards the finishing line at 2-0 up in the next set. Despite that Kumar kept his hopes alive with a 64 finish to make it 2-1 and put the pressure now on Dolan to finish it off.
'The History Maker' sealed it though to set up a clash in the second round with Gary Anderson in a game he will be confident of winning.
Click here for more information on the PDC World Championship, which takes place at the Alexandra Palace between December 13 and January 1.
Kyle Anderson (89.56) 3-2 (83.16) Xiaochen Zong (R1)
Ross Smith (87.67) 0-3 (90.08) Ciaran Teehan (R1)
Brendan Dolan (97.35) 3-0 (90.17) Nitin Kumar (R1)
Ian White vs Darius Labanauskas (R2)
https://twitter.com/OfficialPDC/status/1206237563972919302?s=20