The UK is a notable outlier among the club of mainly rich nations which the OECD represents.
It credited tax cuts in the United States, the world's largest economy, for much of the upgrade - though the global forum warned that protectionist policies were a big risk factor in the forecast.
Fiscal easing in Germany's coalition agreement was seen lifting growth in the euro zone's biggest economy to 2.4 percent this year (+0.1 percentage point) and 2.2 percent in 2019 (+0.3).
This is up from a forecast last November of 3.7% in 2018 and 3.6% in 2019.
The OECD also warned of risks linked to the Group of 20 countries having total debt amounting to over 200 per cent of economic output, and stock valuations being at their highest since the early part of the century. Britain will be the slowest growing major economy, expanding just 1.3 per cent, with investment slowing "amidst continued uncertainty" about Brexit.
With tax cuts boosting the economy this and next year, the OECD forecast the upper bound of the target federal funds rate could reach 3.25 percent by the end of 2019 from 1.5 percent now.
"We should also make full use of the help available from other markets, of other investors, of other scientists, of other technologies to complement our own", he said.
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Growth will particularly be powered by private investment and trade picking up on the back of strong business and household confidence, the OECD said.
"Safeguarding the rules-based worldwide trading system is essential to prevent the longer-term harm to growth prospects that could arise from a retreat from open markets", it said.
Last week, President Trump signed controversial orders imposing heavy tariffs on steel and aluminium.
But its brighter outlook came with a major caveat in the wake of the US decision to slap import tariffs on steel and aluminum and the threat of retaliation by China, the European Union and others.
A full-blown trade war could cost the global economy US$470 billion by 2020, according to analysis by Bloomberg Economics.
"Any escalation, any retaliation or a tit-for-tat type of scenario would be very damaging", he said.
"Countries should rely on collective solutions like the Global Forum on Steel Excess Capacity to address specific issues".