In her maiden speech, Black, the youngest MP in the Commons, attacked the Conservative Party as the most "uncaring, uncompromising and out of touch governments that the UK has seen since Thatcher".
And criticising George Osborne's welfare cuts for young people, she noted that as an MP with a housing allowance she was "the only 20-year old in the UK the chancellor is prepared to help with housing".
Black delivered one of the landmark moments of May's election when she defeated Labour's election campaign chief Douglas Alexander to win the Paisley and Renfrewshire South seat. On May 7 the SNP won all but three of Scotland's 59 constituencies - leaving Labour with just one.
SNP MPs filled their section of the chamber to hear Black speak and were told off for loudly applauding their colleague after she pleaded with Labour's interim-leader Harriet Harman to oppose Osborne's cuts to tax credits.
"I have sat in this chamber for ten weeks and I have very deliberately stayed quiet and have listened intently to everything that has been said. I have heard multiple speeches from Labour benches standing to talk about the worrying rise of nationalism in Scotland," she said.
"All these speeches have served to do is demonstrate how deep the lack of understanding about Scotland there is within the Labour party.
"I, like so many SNP members, come from a traditional socialist Labour family and I have never been quiet in my assertion that I feel it is the Labour Party that left me, not the other way about.
"The SNP did not triumph on a wave of nationalism, in fact nationalism has nothing to do with what has happened in Scotland.
"We triumphed on a wave of hope. Hope that there was something different, something better, to the Thatcherite neoliberal policies that are produced from this chamber. Hope that representatives could genuinely give a voice to those who don't have one."
Despite insisting that nationalism was not the cause of the SNP's rise, she drew laughter when she pointed out William Wallace was born in her constituency
"I don't mention this in order to pour salt into the wounds, which I am sure are very open and very sore for many [Labour] members on these benches, both political and personally, colleagues possibly friends lost their seats," she said.
"I mention it in order to hold a mirror to the face of a party that seems to have forgotten the very people it was supposed to represent, the very things it was supposed to fight for."
Labour in currently engaged in a tense internal row over whether or not it should oppose Osborne's cuts to tax credits. Harman initially indicated the party would not vote against the measures, but three of the four candidates to succeed Ed Miliband as leader have criticised her position.
Black said: "After hearing the Labour leader's intention to support changes of tax credits that chancellor has put forward I must make this plea in the words of one of your own and personal hero of my own."
Quoting from Tony Benn, Black said politicians were either signposts or weathercocks. While weathercocks swung in the wind, signposts, she said "stand true and tall and principled and they point in a direction and they say 'this is the way to a better society'".
Black added: "The only people worth remembering in politics are signposts."
Addressing Labour MPs in the chamber, she said: "Yes we will have political differences, yes in other parliaments we may be opposing parties, but within this chamber we are not .
"No matter how much I may wish it the SNP is not the sole opposition to this government. But nor is the Labour Party. It is together, with all the parties on these benches, that we must form an opposition and in order to be effective we must oppose not abstain.
"I reach out a genuine hand of friendship which I can only hope will be taken. Let us come together. Let us be that opposition, let us be that signpost of a better society."
Black's speech was greeted with loud applause from SNP MPs - who were promptly told off. Clapping is not allowed in the Commons chamber.
Labour MPs were also impressed. London MP Tulip Siddiq, also elected in 2015, said: "I may not agree with everything Mhairi Black said in her maiden speech but credit where it's due -it was well delivered, passionate & witty."