The heated exchange came as the First Minister and her opposition counterpart clashed over the issue of the attainment gap in Scottish schools.
After Ms Davidson accused the SNP of repeatedly failing to improve the quality of Scotland’s education system since the party took power 14 years ago, Ms Sturgeon retorted that she was “pleased” her opponent was no longer focussing on “smears”.
She said: “Ruth Davidson could have chosen to ask me about education in any one of the previous weeks instead she has chosen to indulge in smears, instead of focusing on the issues that people want.
“So I'm actually pleased that Ruth Davidson is back on the issue of education and attainment - in, of course, what is her last FMQs before she goes to the unelected House of Lords.”
The former Scottish Conservatives leader received a peerage in July last year and will not seek re-election to the Scottish Parliament in May.
Ms Sturgeon also repeated that attack in a later remark, stating that: “while Ruth Davidson is off taking £300-a-day to sit in the unelected House of Lords, those of us in this chamber will be getting on with the job of improving education for all.”
The comment prompted outgoing presiding officer, Ken Macintosh, to warn the First Minister.
He told MSPs: “I appreciate this is a political exchange - I always allow some latitude - but the First Minister twice mentioned the House of Lords. I think the point has been made.
He added: “I know that it's a political exchange. I get it. I do understand it. However, the point has been made and I’d rather it wasn't so personal.”
Rising again to speak, Ms Davidson said Mr Macintosh’s intervention was “gallant” but “not required.”
Despite the warning, Ms Sturgeon went on to say she “genuinely” wished Ms Davidson had a “happy time in the House of Lords.”