The final game in the round of 32 was just minutes old when Colombia forward Jhon Córdoba appeared to hurt his groin, forcing coach Néstor Lorenzo to bring Suarez off the bench.
In the 14th minute, Suarez played a sharp ball across the front of the goal where Arias was waiting to flick it past Ghana goalkeeper Lawrence Ati Zigi for a 1-0 lead.
The early goal was a good omen: Colombia have won 11 consecutive World Cup matches when scoring first. Now, they will play Switzerland on Tuesday in Vancouver, British Columbia, for a spot in the quarter-finals.
Los Cafeteros thought they had doubled their lead in the 56th minute, when Luis Díaz found the back of the net only to see the offside flag raised, and the fleet-footed forward had a point-blank shot saved by Zigi a few minutes later.
Zigi wound up making seven saves to keep Ghana in the game.
"We have won absolutely nothing," Díaz said. "These games are very difficult. Every game we've seen has been tight. The good thing and the positive thing is that we're playing very well, we feel comfortable, we are being a family, we are working as a team, and that will work for what is coming."
Ghana were one of a record nine teams from Africa to escape the group stage of the World Cup. And while many gave fits to some of the tournament favourites - hello, Cape Verde against Argentina - only Morocco and Egypt were able to reach the round of 16.
"Sometimes it happens in football that it doesn't go your way," Ghana defender Jerome Opoku said. "It's always great to get out of your group, obviously we wanted to go further."
It was 31 degrees with a heat index of 96 when the game kicked off at Arrowhead Stadium at 8.30pm and the hydration breaks became a blessing as players from both sides fought through dehydration and cramps.
Colombia had breezed through the group stage, conceding only a single goal in wins over Uzbekistan and Congo and a draw with Portugal. Los Cafeteros had been so impressive that Spain coach Luis de la Fuente - whose own team are considered among the tournament favourites - tapped them as "a candidate to win the World Cup."
Their fans certainly believe in them and the stadium was awash in the vibrant yellow of Colombia.
Ghana knew they would be an underdog. Yet the team that failed to qualify for the Africa Cup of Nations last year for the first time in nearly two decades had already answered plenty of critics by surviving a difficult group topped by England and Croatia.
The question as they faced Colombia: Could Ghana mount enough on attack?
As expected, Los Cafeteros dominated the ball - the Black Stars had possession just 36.1 per cent of the time in the group stage, second-least of any team that advanced, and those offensive issues continued against Colombia.
Even when Ghana managed to put together an attack, Colombia were there to quickly counter with the speed of Suárez, Díaz and their midfielders.
Ghana wound up taking eight shots. None of them were on goal.
World Cup last 16 match-ups:-
July 4: Canada v Morocco in Houston and Paraguay v France in Philadelphia
July 5: Brazil v Norway in East Rutherford, New Jersey and Mexico v England in Mexico City
July 6: Portugal v Spain in Arlington, Texas and United States v Belgium in Seattle
July 7: Argentina v Egypt in Atlanta, Georgia and Switzerland v Colombia in Vancouver.
