"Theresa May's had the worst election campaign we've seen in a long, long time". The first minister chastised Dugdale, saying she was entitled to change her mind but not to attack others who sincerely believed in independence.
Sturgeon added: "You [Dugdale] used to agree with me on that". "I think in all honesty none of us actually know at the moment", Sturgeon said.
"I've said it pretty frankly in this one - if the arithmetic allowed it I would want to be part of a progressive alternative to a Tory Government".
Meanwhile, Scottish Secretary David Mundell said rhere will be no second independence referendum in the five years of the next parliament, as it could take until 2022 for Brexit to "play out".
"If one thing has become clear over the course of this campaign, is that Theresa May's not very good at sticking to positions. But what I don't think any politician is entitled to do is to deny the people in Scotland a choice about their future".
Ms Dugdale said: "If the last 24 hours show us anything, it is that the First Minister will say anything to deflect from the SNP's appalling record in office".
In the election debate on Tuesday, Ms Sturgeon said the Scottish Labour leader had told her the vote for Brexit in June 2016 "changed everything" and "Labour should stop opposing a referendum".
Ms Dugdale had earlier fended off criticism Labour leader Jeremy Corbyn would grant a second independence referendum, insisting Labour's manifesto had ruled it out.
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"The contrast with [Labour leader Jeremy] Corbyn is he'll still do a deal with them and that is the message for anybody thinking of voting Labour - Corbyn would do a deal with the SNP".
She said Ms Dugdale had agreed with her that the decision to leave the European Union laid the grounds for a new vote on Scottish independence.
Willie Rennie, the Scottish Liberal Democrat leader, called on Ms Sturgeon to "cancel" another referendum, saying Scots are "sick" and "fed up" of the issue.
A senior SNP source told BuzzFeed News after the debate that Dugdale had previously spoke publicly about the conservation, but that she had missed out a "key part" when talking about it - the part which Sturgeon revealed tonight.
The SNP leader said: "We face decisions around pubic spending which will determine whether or not public spending for our health service, our education system goes up or down".
Ms Sturgeon said many people had been "appalled" by the policy, which she said would save £300 million from the benefits bill at the same time as the Conservatives spend £380 million on a tax cut for the richest 15%.
Sir Michael Fallon did it in 2015 when he accused Ed Miliband of stabbing his brother in the back, and the First Minister borrowed the idea last night to tackle Kezia Dugdale at knee-height as the Labour leader was pressing her over her record at Holyrood.
"This is about limiting child tax credits to the first two children, but it means that for example people who have been raped aren't affected by that, it means they get to have that extra help".