Kai, Wambach and O'Reilly scored in an 11-minute span before Rodriguez, a second-half sub, finished the scoring in the 90th minute. All four U.S. goals came with stiff winds at its back.
Norway needed to beat the USA to win the group and had its chances in the first half when Ingvild Stensland hit the crossbar and goalie Nicole Barnhart stopped Isabell Herlovsen's breakaway.
The Americans are now 6-0 under Coach Pia Sundhage, who said it was good to be tested in the first half.
"I said after the game that I was very grateful because this game taught me a lot," she said. "The fact that you played 45 difficult minutes, and if you can remember how that felt, and if you believe what you are doing, and continue what you do, then you can go out there in the second half and do well. Look at Carli [Lloyd], for instance. She struggled a little bit in the first half, but she and her teammates made it look good in the second half. That's something we are looking for to gain confidence by playing our game."
Denmark was the Group A winner after defeating Finland, 1-0. The final will be a rematch of last year's Algarve Cup final, won, 2-0, by the United States.
March 10 in Alvor
USA 4 Norway 0. Goals: Kai 55, Wambach 57, O'Reilly 65, Rodriguez 90.
USA -- Barnhart, Buehler, Markgraf, Rampone (Whitehill, 75), Chalupny (Cox, 75), Boxx (Osborne, 63), Lloyd, Woznuk (Tarpley, 46), O'Reilly (Heath, 70), Kai (Rodriguez, 63), Wambach.
Norway -- Hjelmseth, Horpestad, Folstad (Lund, 58), Nordby, Vikestad, Stensland, M.Knutsen, Storlokken, Herlovsen, Wiik, Kaurin (G.Knutsen, 68).
Referee: Bibiana Steinhaus (Germany).
Algarve Cup Results:
Denmark 1, Germany 0
Sweden 3, Finland 1
Germany 3, Finland 0
Denmark 1, Sweden 0
Denmark 1, Finland 0.
Germany 2, Sweden 0
Standings: Denmark 9 points; Germany 6; Sweden 3; Finland 0.
USA 4, China 0
Norway 4, Italy 2
USA 2, Italy 0
Norway 3, China 1
USA 4, Norway 0
Italy 2, China 0
Standings: USA 9 points; Norway 6; Italy 3; China 0.
Iceland 2, Poland 0
Portugal 2, Ireland 0
Portugal 3, Poland 1
Iceland 4, Ireland 1
Iceland 3, Portugal 0
Ireland 1, Poland 0
Standings: Iceland 9 points; Portugal 6; Ireland 3; Poland 0.
Algarve Cup Placement Matches
Poland vs. Ireland: 11th-Place Match
Portugal vs. China: 9th-Place Match
Iceland vs. Finland: 7th-Place Match
Sweden vs. Italy: 5th-Place Match
Germany vs. Norway: 3rd-Place Match
USA vs. Denmark: Championship