The BNZ-Business New Zealand Performance of Services Index rose 2.7 points last month to 51.6, which indicates the sector is expanding.
Any reading in the index below 50 points to contraction.
The index was led higher by growth in sales, stocks, and new orders, with the latter jumping to 60.1 in March from 55.3 in February.
BNZ senior economist Craig Ebert said this pointed to an underlying resilience in demand, after the initial shock of Omicron's spread.
However, there were also signs that firms were hamstrung by skills shortages and supply chain disruptions, with the employment and supplier deliveries sub-indices sitting below the break-even mark of 50.