In Rome, they trailed 10-0 before coming through 27-24 against Italy and they fell 14-5 down to Wales at halftime before overhauling them 16-14 thanks to a Fraser Dingwall try and the boot of George Ford.
"This is a team which stays in the fight, which finds a way. It is a young side and we have a lot to learn, but we will grow together," Borthwick said.
"At half-time we were very composed and clear. There was great leadership from Jamie (George). There was a determination to find a way and we had belief we would do. Our defence was excellent, there was control there, and there was some development in our attack.
"Against Italy we went to the edge 17 times and today we were not too far short of that on a greasy day - we showed some progress."
Despite receiving two early yellow cards, Borthwick also hailed England's discipline as they gave away only one penalty in the second half, adding to six in the first, when Wales had not been penalised at all.
"We gave away eight last week and Maro Itoje set a target of seven this week," he said. "So to achieve that, after a 6-0 penalty count against us in the first half was excellent."
Borthwick also praised the impact of his replacements, with hooker Theo Dan and abrasive flanker Chandler Cunningham-South enjoying impressive cameos.
"There were big contributions from the bench," the coach said. "It means you can increase the intensity. Since 2018 England generally had lost their way in the second half but we've seen an improvement in that through the World Cup and now."
England have a break before taking on Scotland in Edinburgh, where they will seek a third championship win for the first time since 2020.
"There was definitely progress from last week," said George after captaining the side for the first time at home.
"In the first half we were under pressure from a good Wales attack but we defended well, often multi-phase. I’d rather not have only 13 men on the field but we showed great fight and discipline.
"We said the bare minimum this England team is going to show is fight and character. There is belief but we can't get too far ahead of ourselves as we know we are going to need to get better."
