Sophia Dunkley put on 92 with Katherine Brunt.
Sophia Dunkley struck an unbeaten 73 in her maiden one-day international innings, and Cross herself claimed five for 34 as England took a 6-2 lead in the multi-format series.
England had made a shaky start in pursuit of a total that looked to be well below par on a good hybrid pitch, men Tammy Beaumont and Heather Knight fell early on for just 10 runs apiece.
But Dunkley, who made her ODI debut on Sunday, was able to hold her nerve despite her limited experience and dig in to see England over the line.
Cross said: “I was a bit nervous when we still needed 120-odd to win, however I thought it was amazing to see the likes of Sophia Dunkley and Brunty – a girl who has not batted in ODI cricket, and a girl who has batted a lot in ODI cricket – to put us over the line.
“I thought it was an incredible partnership and it just looked so calm. When they’re calm, I’m not nervous any more, so it was good.”
La hun til: “There was a few nerves around. I think the girls that were padded up were a bit nervous to go in but I think it was just good to show the depth that we’ve got in the batting line-up and that we’re not just reliant on our top four to be scoring the runs all the time.
“Obviously Tammy’s been fantastic for us in our last couple of innings – more than our last couple of innings in one-day cricket – and if she’s not scoring runs it’s great to see that someone else can pick that up and do a job for the team, so it was a pleasing win really.”
In India’s innings, Cross claimed her second ODI five-for, despite having been labelled predominantly a red-ball bowler in her career.
“(Det er) always good to pick wickets up. I’ve always said that sometimes I get the boring, rubbish jobs where you’re bowling into the wind or up the hill and kind of have a holding role that creates pressure at the other end, so it was nice to pick some up myself today,” the Lancashire seamer said.
India captain Mithali Raj again top-scored for India as they put on 221 all out after being put in to bat.