McConnochie got England's day off and running as he crossed for the first of two tries against Russian Federation inside the first minute in a 47-0 win, with 19-year-old Ryan Olowofela also scoring twice in that match - his first every tries at the World Series.
The sensational win was their first in the 2017/2018 World Rugby Sevens Series.
They had been trailing 12-5 after first-half Luciano Gonzalez and Felipe del Mestre tries handed a valiant Argentinian side the ascendancy.
New Zealand then won a crucial turnover with England attacking their line and Vilimoni Koroi burst through a gaping hole with great speed to claim a 12-7 lead at the break.
Fiji scored a last second try to seal the match.
New Zealand will face Fiji in the first semi-final at 4.49pm.
Player of the Final was Fijian flyer Alasio Sovita Naduva who scored three of Fiji's tries in the four tries to three-try victory.
Owira and Ngethe were both on target; with the former scoring two tries while Ngethe put in a try as Shujaa fell to Samoa in the fifth and sixth play-off.
It was not such a smooth run for Fiji who needed their get-out-of-jail card to beat Samoa 12-10 in the quarter-finals with Kalioni Nasoko running 95 metres to score the winning try on the last play of the game.
England, Australia and Samoa also secured quarterfinal places with two wins from three games while Scotland edged Argentina for the other place in the top eight.
Samoa produced their best performance of the season, bouncing back from their quarter final defeat by Fiji to edge England 22-17 in extra-time and Kenya 19-15 in the playoff for fifth place.