The winger scored three times in 21 second-half minutes to draw level with Lomu's mark of 15 World Cup tries.
The Springboks ran in eight second-half tries in all to earn a bonus-point win at the Olympic Stadium.
South Africa top Pool B and will now play the loser of Saturday's Pool A decider between Australia and Wales.
A mixture of South Africa's ill-discipline and poor finishing kept the score down in the first half, while USA only made it into the Boks' 22 in the last minute of the half, despite enjoying plenty of possession.
Centre Damien de Allende scored his first international try before South Africa were awarded a penalty try as USA struggled at the scrum.
A different South Africa came out after the break as Habana scored almost from the restart, collecting a Fourie du Preez kick to go over in the corner.
Bismarck du Plessis and Francois Louw both crossed the line, before Habana scored two tries in two minutes to complete his hat-trick.
Louw scored his second with Jesse Kriel also getting on the scoresheet, before Lwazi Mvovo rounded off a dominant Springboks performance.
Habana had a subdued first half, with his only contribution of note seeing him clatter into Blaine Scully as the pair competed for a high ball.
But he came out firing in the second half and his hat-trick not only saw him equal New Zealand legend Lomu as the tournament's all-time leading try scorer, but also draw level with Australia's David Campese for joint second in the list of Test try scorers with 64.
The 32-year-old, a 2007 World Cup-winner with the Boks, scored 62 seconds into the second half for his 13th World Cup try.
He then went over unopposed in the 59th minute after a break by De Allende and swooped on a loose ball to dive over in the corner just two minutes later.
Habana could have broken All Black winger Lomu's record but a knock-on as he tried to collect another chip through denied him a fourth try on the night.
South Africa's World Cup campaign started in the worst possible way with that shock loss to Japan, but they recovered with a bonus point victory over Samoa and a comfortable win against Scotland.
If they are to win the tournament, they will be the first side to do so having lost a pool match.
Before the USA game, Boks coach Heyneke Meyer talked about his side "doing a Roger Bannister", citing the British runner who broke the four-minute mile barrier as an example of overcoming the impossible.
He also spoke about respecting their opponents but in the first half they showed signs of complacency and failed to pile the points on an under-strength USA, who had made 12 changes from their defeat by Scotland.
A rejuvenated and more clinical Springboks came out after the break - and eight tries in 40 minutes will certainly send out a message to the teams left in the competition.
South Africa: Le Roux, Habana, Kriel, de Allende, Mvovo, Pollard, du Preez, Mtawarira, B. du Plessis, Malherbe, Etzebeth, de Jager, Louw, Burger, Vermeulen.
Replacements: Serfontein for de Allende (60), Steyn for Pollard (56), Paige for du Preez (63), Nyakane for Mtawarira (56), Brits for B. du Plessis (56), du Toit for de Jager (63), Alberts for Burger (48).
Not Used: Oosthuizen.
USA: Scully, Thompson, Niua, A. Suniula, Test, S. Suniula,Kruger, Kilifi, Thiel, Baumann, Stanfill, Trouville, Barrett,Quill, Manoa.
Replacements: Wyles for Scully (70), Moeakiola for Kilifi (58),Taufetee for Thiel (72), Fenoglio for Trouville (70), McFarland for Barrett (57), Dolan for Manoa (48).
Not Used: Lamositele, Petri.
Attendance: 54,658
Referee: Pascal Gauzere (France)
Bryan Habana equalled Jonah Lomu's World Cup try-scoring record with a hat-trick as South Africa reached the quarter-finals by thrashing USA.