Opener Jadhav (113) also scored a century and put on 155 runs for the third wicket with Kaif (103 not out). The senior team's bowlers, Irfan Pathan (1/55), Zaheer Khan (1/31) and Anil Kumble (1/57), struggled to make an impression.
India 'A', who made 302 in their first knock, declared at 297 for five in their second essay in the last session with ten overs remaining to be bowled on the penultimate day of the four-day practice match at M Chinnaswamy Stadium here.
That left Sourav Ganguly-led India Seniors, who made 213 in their first innings conceding a 89-run lead to the rivals, to score a challenging 387 for victory. At stumps, they were 35 without loss with Yuvraj Singh batting on 23 and Virender Sehwag on 12.
The day belonged to the Maharashtra batsman Jadhav and Kaif who frustrated the senior bowlers. Jadhav hit eleven fours in his 221-ball knock before being adjudged lbw to Kumble. Kaif scored his runs off 194 balls with 12 boundaries and a six.
The hallmark of the 284-ball third wicket stand between Jadhav and Kaif was the excellent running-between-the-wickets which was a delight to watch.
Kaif, who has made no secret of his goal to get into the Test squad, brought up his century in style with a lofted boundary off Virender Sehwag. Earlier, he hoisted Harbhajan Singh for a straight six.
Harbhajan, looking for some useful bowling practice ahead of the first Test against Aussies commencing here on October 6, went wicket-less in 20 overs that he bowled.
In fact, Sidharth Trivedi turned out to be the most successful bowler for India Seniors, taking two wickets for 52 runs.
Earlier, India 'A' skipper Dinesh Mongia was the first to go in the morning when the side resumed from their overnight 47 for one, caught in the slips by Rahul Dravid off Trivedi for 25.
Then came that long partnership before the departure of Jadhav. M S Dhoni (12) and Joginder Sharma (11) were dismissed cheaply. When declaration came, Kaif and Venugopal Rao (20 not out) were involved in a 44-run unbroken partnership for the sixth wicket.
Chasing the victory target of 387, Virender Sehwag, desperately looking for a big knock after the recent poor runs, started off with a boundary of S S Paul and then raised his bat in the direction of John Wright, sitting in the players stand, who acknowledged it with a smile.
India 'A': 302
India Seniors: 213
India 'A' second innings: (47 for one overnight)
Dheeraj Jadhav lbw b Anil Kumble 113
Gautham Gambhir c S Ganguly b Zaheer Khan 0
Dinesh Mongia c R Dravid b Sidharth Trivedi 25
Mohammed Kaif not out 103
M S Dhoni c Harbhajan Singh b Irfan Pathan 12
Joginder Sharma c R Dravid b S Trivedi 11
Venugopal Rao not out 20
Extras (8b, 3lb, 2nb) 13
Total (for five wickets declared, in 93 overs) 297
Fall of wickets: 1-6, 2-58, 3-213, 4-234, 5-253.
India Seniors bowling: Pathan 13-2-55-1; Zaheer 12-3-31-1; Trivedi 20-4-52-2; Harbhajan 20-3-61-0; Kumble 19-2-57-1; Sehwag 7-0-24-0; Yuvraj 2-1-6-0.
India 'A' second innings:
Yuvraj Singh batting 23
Virender Sehwag batting 12
Total (for no loss, in ten overs) 35
India 'A' bowling: Amit Bhadari 2-0-14-0; S S Paul 4-0-18-0; Murali Kartik 3-1-3-0; Venugopal Rao 1-1-0-0.