Much or all of the extra investment would be recovered from savings on oil imports, the Commission said in its 'roadmap for moving to a competitive low-carbon economy in 2050'.
Unrest in the Middle East and North Africa has sent oil prices higher, hitting shares in European companies.
"As oil prices keep rising, Europe is paying more every year for its energy bill and becoming more vulnerable to price shocks. So starting the transition now will pay off," said Connie Hedegaard, the EU's commissioner for climate action.
Europe has to invest an extra 1.5% of its economic output each year to rein in energy costs, the Commission's report said.
Most controversially, the roadmap said that meeting efficiency goals would also help the bloc beat existing targets for cutting greenhouse gas emissions by the end of the decade.
The European Union has a long-term goal to slash emissions by 80% below 1990 levels by the middle of the century and to trim greenhouse gases by a fifth by 2020.
The EU would cut greenhouse gases by a quarter by the end of the decade, if it met renewable energy and efficiency targets by then, the Commission said.
The notion of beating the 2020 goal was criticised in equal measure for going too far and not far enough by business and green groups respectively, a battle likely to complicate the plan's adoption by member states in the coming months.
The EU has long said it could move to a more ambitious, 30% emissions cut if other countries also offered more ambitious action in currently deadlocked UN climate talks.
The EU has a non-binding target to improve efficiency by a fifth by 2020, and the Commission published a separate report on Tuesday detailing how to meet the goal.
One way of boosting efficiency would be to cut the quota of emissions permits to industry in Europe's carbon market, the Commission said, tightening the emissions trading scheme's (ETS) screw on greenhouse gases.
The market caps emissions from factories and power plants by issuing a fixed quota of permits, now in surplus after a financial crisis cut pollution and halved the carbon price.
Setting aside a "gradually increasing" number of carbon permits from 2013 to 2020 could push carbon prices higher and drive low-carbon investment, the Commission said.
The 'BusinessEurope' industry lobby opposes that idea, saying it would hurt companies whose rivals in China, Japan and the United States face less onerous climate laws.
(EurActiv with Reuters.)