Resuming the day three at one for no loss, Singh (118) and Rasool feasted on a placid Nehru Stadium wicket as the two rattled a 198-run partnership for the third wicket to put J&K in a commanding position.
J&K openers, Singh and Adil Rishi (51), provided a solid start to their team as both added 71 runs in 20 overs before the latter fell to left-arm spinner J Syed Mohammad going for an extravagant shot.
Next man-in, Bandeep Singh (19) did not last long as he was caught by wicketkeeper Kunal Saikia off pacer Abu Nechim Ahmed.
Singh and Rasool then combined well and treated the opposition bowlers with disdain to tighten their grip on the match. The contest turned out to be a one-sided affair as both pummelled the hosts' bowling attack with their resolve and determination.
Assam used as many as six bowlers to get a breakthrough but luck eluded them till the 61st over when off-spinner Arlen Konwar had Singh caught by subsitute A S Sinha. Singh's 156-ball innings was laced with 15 fours and two sixes.
In the process, Rasool also completed his third first-class hundred. His aggressive unbeaten 106-ball knock was studded with 17 fours and two sixes.
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J&K declared their second innings at 318 for five in 66 overs with an overall lead of 476 runs.
Chasing 477 runs, the visitors reduced the hosts to 46 for three by stumps with pacer Ram Dayal dismissing opener Pallavkumar Das (0) and Kunal Saikia (0) in his successive overs.
Bandeep Singh got rid of Sibsankar Roy (29) as Assam were left reeling at 46 for three with skipper Dheeraj Jadhav (16 batting) and Gokul Sharma (0) at the crease.