According to official figures released on Tuesday, excluding bonuses, pay growth was up to 3.4% from 3.3%, beating all forecasts.
Forecasts had expected a slip in average earnings, excluding bonuses, to 3.1%.
The wage growth was boosted by a 3.8% annual jump in pay for April alone - the largest single-month rise since May 2008, the Office for National Statistics said.
Unemployment fell by 34,000 to 1.3 million in the three months to April, meaning the jobless rate was unchanged at 3.8% - its lowest rate since January 1975.
The number of people in employment rose by 32,000 to 32.8 million, the smallest increase since the three months to August last year, as employers increasingly say it is hard to find staff.
But the UK labour market so far appears to have bucked any uncertainty around the timing and terms on which Britain will leave the European Union, in contrast to other parts of the economy.
Official figures on Monday showed the economy shrank by 0.4% in April, its biggest monthly drop since 2016.
Employment minister Alok Sharma said: "Once again we see more people in work than ever before; 3.7 million more since 2010.
"With wage growth increasing pace on last month, outstripping inflation for the 15th month in a row, and record high female employment - the government's focus on pro-business policies and balanced economic management is delivering opportunity for all."
Matt Hughes, head of labour market statistics at Globelynx, said: "Overall, the labour market continues to be strong, with employment still at a joint record rate.
"However, while the number of vacancies remains high, it has fallen back slightly from the historic highs seen at the turn of the year.
"The overall gap between men and women in hours worked is now the lowest ever - women now average about three-quarters of men's weekly hours, compared with around two-thirds 25 years ago."