Krishna took 5-23 in his 8.2 overs as Afghanistan were bowled out for 218 in just 44.2 overs on Saturday after the visitors had won the toss and opted to bat in Chennai.
Skipper Hashmatullah Shahidi scored 102 off 131 balls but didn't get enough support.
In reply, India were never in any trouble as Jaiswal struck his second ODI hundred, while also putting up 170 for the opening wicket with Rohit Sharma.
Sharma scored 79 off 69 balls and Jaiswal was unbeaten in the finish as India wrapped up the game on 1-224 in 28.4 overs, winning with a whopping 21.2 overs to spare.
India had already clinched the series, the first-ever bilateral three-game ODI contest between the sides, with a 170-run win in the second match at Lucknow and a seven-wicket victory in the rain-shortened first match at Dharamshala.
Earlier, Krishna had struck quick blows with the new ball, Afghanistan losing four wickets in 9.2 overs.
Sharma aided Krishna with his initial burst and took three catches at slip as Afghanistan plunged to 4-36.
Shahidi then saved the day for Afghanistan, anchoring his side with a maiden ODI century off 128 balls, hitting 13 fours and a six, as he shared a 105-run stand for the fifth wicket with Azmatullah Omarzai, who hit 50 off 56 balls.
Jaiswal and Sharma made light work of the chase. Jaiswal scored 50 off 38 balls with seven fours and a six, then hit another six and six fours to score his second 50 off the next 45 balls.
Sharma scored his 61st half-century off 47 balls, but fell close to the century mark, out caught off Nabi in the 23rd over.
Jaiswal and Shreyas Iyer (20 not out) added a quickfire 54 off 35 balls to race across the finish line.
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