Dunkley's innings helped England recover from 92-4 in their pursuit of 222, with the young Surrey star seeing England home with 15 balls to spare and ensuring a five wicket victory.
Earlier in the day England's Kate Cross took an impressive 5-34 as India struggled to get going with the bat again and failed to get a substantial enough total to truly test the hosts on a good Taunton wicket.
Cross takes five as India struggle with the bat again
Having scored just 201-8 in the first ODI at Bristol, the Indian batters appeared to come out with a new attacking mentality after being put into bat by Heather Knight at the beginning of play.
Both Smriti Mandhana and Shafali Verma found the boundary early on with Verma in particular going after Kathrine Brunt's first spell, twice pulling her away to the deep backward square leg boundary in the opening stages.
By the end of the powerplay the Indian openers had reached an unbroken 50 stand with the side looking set to post a solid first innings total.
This good start, however, came to end when Mandhana chopped onto her stumps while trying to guide the ball down to third man off the bowling of Cross for a score of 22.
Her dismissal was swiftly followed by both Jemimah Rodrigues and Verma who fell to Sophie Ecclestone and Cross respectively, with India quickly falling from 56-0 to 77-3.
Over the next 18 overs, though, captain Mithali Raj and veteran Harmanpreet Kaur began to rebuild the innings as they looked to carefully rotate the strike, eventually bringing the score to 145-3 in the 34th over.
Raj and Kaur had begun to frustrate the England bowlers but their partnership was eventually broken when Kaur skied one high in the air off the bowling of Cross who then took a comfortable catch off her own bowling for 19.
Raj continued to bat through but struggled to find a partner who could hang around with her, Deepti Sharma going next for just five, falling to impressive Cross when she was well caught in the deep by Dunkley.
Sneh Rana would quickly follow, going for five when she chipped one up to Knight at mid-on, again off the bowling of cross and completing her five-for.
The 29-year-old bowled with extreme precision throughout the innings and was justly rewarded for her superb line and length with her second five wicket bag in international cricket.
And with this the Indian innings continued to fade away, Taniya Bhatia and Shikha Pandey both losing their wickets in the following overs, each heading back to the pavilion having added just two to the score.
The big wicket of Raj was next to come though, with her being run out for 59 after she failed to make her ground while attempting to steal an extra run following misfiled in the deep by Dunkley, who made up for her mistake with an excellent throw back into wicketkeeper Amy Jones leaving India 194-9 in the 47th over.
The final pair of Jhulan Goswami and Poonam Yadav did manage to cause the England bowlers some bother though, eventually taking the score to 221 before Yadav was clean bowled off the last ball of the innings by Ecclestone.
Brilliant Dunkley helps England survive nervy finish
The England batters went out looking to recreate the drama free chase they produced in the first ODI and it looked as if they would do just that when openers, Tammy Beaumont and Lauren Winfield-Hill, played a pair of stunning off drives during Goswami's opening over.
When the in-form Beaumont was clean bowled by a perfect seaming delivery from Goswami for 10 in the fifth over, however, it became quickly apparent that this chase would be somewhat more challenging chase than the one at Bristol three days ago
Captain Knight joined Winfield-Hill at the crease and, thanks to some excellent work from the Indian opening bowlers, the two struggled to find the boundary with any regularity and England ended to powerplay on a score of just 37-1.
Frustration over the lack of runs began to come to the surface and Knight fell victim when she attempted to hit Yadav straight back over her head but could only find Goswami at mid-off, losing her wicket for only 10 runs.
For a time it looked as if Nat Sciver and Winfield-Hill would be able to rebuild the England innings and still make the chase relatively simple.
That was until Winfield-Hill had to depart for a well made 42 when she edged one behind off the bowling of Panday.
Things would then get worse for England when Sciver was also caught behind by Bahatia just two overs later for 19, this time while facing Rana, leaving England in trouble at 92-4 and bringing youngster Dunkley the crease.
Her partner, Amy Jones, was able to reduce some of the scoreboard pressure on England, with the wicket-keeper making a quick-fire 28 off 34 balls before eventually being caught after hitting one straight up in the air while trying to clear the boundary against Yadav.
As the sun began to set in Somerset the on-debut Dunkley continued to battle on through, showing a level of composure far beyond a player of her experience and gradually whittling down the required runs.
Despite the pressure of the situation the 22-year-old gave the tourists little chance of getting her out at any point during her innings, the highlight of which was without doubt a stunning six she launched over wide-long-on off the bowling of Pandey.
Dunkley, who finished just 27 short of a century, was also well supported by Brunt at the other end who finished on 33 not out with the two putting on a stand of 93 runs and eventually seeing their side home with 2.3 overs remaining.
The result means England have secured victory in the ODI portion of the tour and take a 6-2 lead in the multi-format series.
The series between England and India continues with the final ODI taking place on Saturday at Worcester.