The Red Rose saw wing Elliot Daly sent off after just four minutes for tackling Leonardo Senatore in the air, but they did not wilt under their task, with Owen Farrell keeping the scoreboard ticking over from the kicking tee.
A penalty try extended their lead but tries from Facundo Isa and Santiago Cordero cut the gap to two points.
Jonny May then boosted the advantage and with Farrell continuing to excel, prop Enrique Pieretto joined Daly in the changing rooms four minutes from time after being given his marching orders for stamping on Joe Marler.
The victory was England's 12th in a row and maintained their perfect record under Jones.
Speaking afterwards, the Australian hailed the flexibility shown by his players after going down to 14 men, reserving special praise for the effort from his forwards.
"Our team was brilliant today," Jones told Sky Sports. "The way we adapted our tactics and coped with the problems was tremendous and the senior players were outstanding.
"I think we won the match before half-time. The way we held on with those scrums was superb. It was 15 men against 13 of a rugby league team, but we coped."