The Irish Grand Slammer is one of only five players, all from Magners League clubs, to have been selected for all three Tests - skipper Paul O'Connell, Tommy Bowe, Stephen Jones and Mike Phillips are the others - and he wants to end the tour on a high after two devastating defeats in the earlier Tests.
"This gamed is all about and I don't think we'll have any problem replicating the desire and intensity that you saw in Pretoria. It's all about the Lions jersey and the many great players who have come before us," said Heaslip.
"We owe it to them to avoid the whitewash."
The Lions were crushed by a last second penalty from 54 metres by Morne Steyn last weekend in Pretoria that gave the Springboks a 28-25 victory - and the series 2-0. In Durban the week before Heaslip and co had battled back to within one score before going down 26-21.
"We've got to reduce the mistakes and stick to our multi-phase game. When we've done that, they've battled to keep up with us," said Heaslip.
"We must keep up the intensity. We made two mistakes last week and they punished us, but that's what world champions do.
"They're very brutal up front and, as you can see from our injuries, in the backs as well. I've been involved in a few tough games in the past, but I've never experienced anything like last weekend's Test."
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