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Monaco star Rodriguez hit a stunning dipping volley to open the scoring in the first half before sealing his side's 2-0 victory -- and setting up a meeting with hosts Brazil -- when he sidefooted home soon after the break.
The 22-year-old's double strike made him the World Cup's top scorer with five goals, one ahead of Argentina's Messi, Brazil's Neymar and Germany's Thomas Muller, and Tabarez said he believed he was the tournament's best player.
"For me, talents are those who do things that have nothing to do with their life experience," he told reporters after the match.
"Diego Maradona, Lionel Messi, Luis Suarez and James Rodriguez -- they do things because they have a certain gift which makes them special.
"It is not up to me, but I believe from what I have seen that he is the best player in the World Cup."
Colombia coach Jose Pekerman said he had "never had any doubts that this was going to be his World Cup" and added: "I greatly praise what he is doing.
"What is most surprising is that, at his young age, he does not have any objection, any problem in being responsible for doing things that football players take many years to understand.
"Football forces you to deal with a lot of situations, you have to handle these situations -- and we have a technical player who has every attribute of a top-notch player at a world level."
Rodriguez, who has joined Monaco from Porto for 38.5 million pounds -- the second most expensive Colombian footballer after teammate Radamel Falcao -- has starred for his country in the injured Falcao's absence.
He said: "I only want to help so that the team can win. I want to do my share so Colombia can go far. I'm at a good level and we are scoring goals. I'm very happy about that."
His career began in his home country with Envigado before he moved to Banfield in Argentina in 2009 and then to Porto the following year. He scored a hat trick in the 2011 Portuguese Cup final and won the country's 2009 Golden Ball award the following year, becoming the youngest player ever to do so.
Player of the day: James Rodriguez
James Rodriguez steals the day, scoring a brace to bring his total up to five in his first four World Cup matches.
Colombia continue to impress
ESPN's Alexi Lalas and Santi Solari discuss Colombia's 'confident' performance against Uruguay and reflect on James Rodriguez's stunning goals.