Luckily for Gunn, teammate Anya Shrubsole clean bowled Rajeshwari Gayakwad the next ball to secure England's fourth World Cup title.
India, chasing a modest 229 to win, was cruising to victory in the final as it reached 190 for three. But a late collapse, sparked by five wickets in 19 balls from Shrubsole, saw England snatch an unlikely victory on home soil.
"It was just an unbelievable game. We looked for minute like we were out of it," Shrubsole said. "But one of the great things about this team, we never give up. We never let the run rate get away from us, even though we weren't getting wickets. We knew if we got a couple we'd be right in the game and all was well in the end.
"I think it's a dream and a dream you never think is going to come true."
It was a milestone moment for women's cricket as Lord's - known as the Home of Cricket - was sold out and ticket scalpers were outside the ground.
The English had lost to India in their opening game of the tournament but impressive victories in the next six matches made them favorites to add to the cups they won in 1973, 1993 and 2009.
England captain Heather Knight won the toss and chose to bat first, but she had departed for one when Natalie Sciver arrived in the middle with England 63 for three.
Sciver and Sarah Taylor put on 83 for the fourth wicket, but both were casualties of a stunning spell of three wickets for two runs off 10 balls by fast bowler Jhulan Goswami. Sciver, the only player to make two centuries at this World Cup, reached another 50, but added just one more run before she was trapped by Goswami.
Katherine Brunt made a breezy 34 and Jenny Gunn an unbeaten 25, but England's total of 228 for seven appeared distinctly reachable for India.
Shrubsole got England off to a dream start as India began their reply, nicking the off-stump of the dangerous Smriti Mandhana for a duck in the second over.
When Mithali Raj got herself run out, by Sciver, going for a single that was never on, India was 43 for two and the encounter was finely poised.
However, that brought Harmanpreet Kaur, who destroyed Australia with a breathtaking unbeaten 171 in the semifinal, to the crease. Kaur clubbed two sixes on her way to 51 before holing out to Tammy Beaumont, off Alex Hartley, going for a third.
But misfields and mistakes were starting to creep in for England. Taylor missed a stumping to get rid of Poonam Raut before Knight dropped Veda Krishnamurthy.
The game seemed up by the time Raut, struggling with cramp, finally fell leg before to Shrubsole for 86, leaving India 191 for four.
But when Hartley accounted for Sushma Verma for a duck, then Shrubsole removed Krishnamurthy and Goswami in successive balls, England had a lifeline.
Taylor thought she had Deepthi Sharma stumped but an drawn-out replay could not prove her foot was off the floor at the point of impact.
Yet moments later Shikha Pandey was run out, Sharma picked out Sciver off Shrubsole and India was nine down.
Shrubsole got the job done clean bowling Gayakwad to spark celebrations on the pitch and bedlam in the stands in north London.
