Caley Thistle and Hamilton will occupy the bottom two places in the Premiership but either could be automatically relegated by ending last.
The second bottom side will go into the Premiership play-off final and meet either Dundee United or Falkirk.
"We need that performance again come Saturday," said Foran.
"It was a real mature performance. Forget about the two fantastic goals, defensively we were magnificent. Dundee must have put 30, 40 crosses in the box, we won every header - credit to the lads.
"We've just put huge, huge pressure now on Hamilton. It's a massive game for them [against Dundee on Saturday], massive game.
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"It's a massive game [for Inverness against Motherwell on Saturday] - one that we look forward to."
Foran's side are a point and five goals worse off than Martin Canning's Hamilton, who lost 3-2 at Ross County on Tuesday, with one game to go.
Both of the bottom two sides are at home on Saturday.
"Players now are playing to their best," explained Foran. "Now, we're in the right place, we're in a good place at the moment. You're still up against a good team in Motherwell. We're confident going into that game.
"We've given ourselves a chance for Saturday now.
"I don't think there's a lot of pressure on us. I think all that pressure's now gone on to Hamilton's shoulders."
Neil McCann sustained his first defeat since taking charge of Dundee, who were assured of Premiership safety by virtue of Hamilton's loss in Dingwall.
"I thought we had turned full circle but I saw a little sign tonight on maybe why we were on such a poor run before," said McCann.
"I think they've been remarkable in the three games that we've played previous to this one in terms of their attitude and drive to get us out a position and I'm delighted we're safe for the club but that isn't acceptable.
"I'm really disappointed with it and I told them that I don't care about staying up, that type of performance is not good enough."
Inverness Caledonian Thistle manager Richie Foran believes the 2-0 victory over Dundee has put "huge" pressure on Hamilton Academical.