Elizabeth Warren and Scott Brown showed why the US Senate race in Massachusetts is one of the most closely watched in the nation, as the two candidates skilfully sparred and jabbed throughout their first debate in what was a toe-to-toe contest.

Both candidates displayed considerable ability as debaters, although Brown, the Republican incumbent, was willing to mix charm with mud-slinging, quickly ridiculing Warren's disputed claims to Native American heritage: "Professor Warren claimed that she was a Native American, a person of colour and as you can see, she's not."

Brown's remark was a reference to a controversy over Warren having represented her heritage without evidence, which Warren blames on "family stories" and denies any professional gain.

Warren remained unflappable in the face of Brown's provocations, and at each point in the fast-moving debate hammered away at Brown's voting record in the US Senate, nailing him to extreme Republican positions on the economy, energy, climate change and women's rights. "Senator Brown can say all he wants. But he has voted," Warren said.

Meanwhile, Brown strained to paint Warren as "obsessed" with raising taxes while trying to show her career in an unflattering light.

On women's issues, Warren pointed to evidence of Brown's voting record as exposing the gap between his words and deeds. But Brown defended himself by saying: "I've been fighting for women's rights when I was six years old when my mother was being abused by one of my stepfathers."

Choosing to address his opponent as "Professor Warren" throughout, Brown's most outrageous remark came towards the end of the debate, when the candidates were asked about graduate unemployment. Brown launched into a rehearsed reply about the high cost of university tuition, which he turned into a reference to Warren's $300,000 salary from Harvard – suggesting that Warren's own pay was the cause of the rising cost of college tuition.

Throughout the debate Brown bristled aggressively while managing to maintain an air of good humour and faint praise, while carefully blending in his support for positions popular in Massachusetts that are opposed by the Republican party nationally, such as abortion.

Brown was eager to damage Warren's resumé, expansively attacking her for her part in asbestos claims settlements that Warren derided as wrong. When Warren voiced support for her former Harvard colleague Elena Kagan as US supreme court justice, and noted that Brown opposed her nomination, Brown sniped: "I'm sorry I didn't vote for your boss."

Warren's response was to yoke Brown to the Republican party of Mitt Romney and climate change deniers such as Senator James Inhofe, pointing out that GOP control of the Senate would put Inhofe at the head of the Senate's environmental committee. "You're not running against James Inhofe, you're running against me, professor" was Brown's riposte.

Neither side could credibly claim victory from the debate. Brown launched a few skyrockets and displayed his everyman image, even mentioning the pickup truck he drove to the debate. Warren, less well-known than the incumbent, gained visibility and showed she had nothing to fear from Brown's attacks. If anything, her earnest demeanour contradicted Brown's efforts to label her a "radical", as he did seven times in the hour.

The pair have three more debates still to come, and on the evidence of this they should be just as entertaining.