April 27 (Reuters) - Visa Inc is emerging from the COVID-19 pandemic, its top boss said on Tuesday, as a surge in online shopping helped the world's biggest payment processor beat Wall Street estimates for quarterly profit and counter sluggish travel spending.

Payment companies are slowly seeing an uptick in volumes from the coronavirus-induced slump as massive government stimulus and the rapid rollout of vaccines fuel an economic recovery, unleashing pent-up demand for both goods and services.

Visa's total payment volumes rose 11% on a constant dollar basis from a year earlier, its biggest jump since the start of the pandemic.

"Visa has weathered the COVID storm and is emerging from the pandemic even stronger," Chief Executive Officer Alfred Kelly Jr told analysts on a call.

The company saw a return to positive growth for credit and card present transactions, while debit and ecommerce also grew, Kelly Jr said in a statement.

U.S. debit cards volumes soared 31% to $806 billion.

However, pandemic restrictions and a resurgence of COVID-19 cases in several parts of the world have forced people and businesses to put travel on hold, sending cross-border volumes at Visa down 11%.

That was still better than the past two quarters, when volumes had crashed.

Chief Financial Officer Vasant Prabhu said the recovery continued despite closed borders, with travel to and from the United States and Latin America providing the biggest boost.

Travel in and out of Asia, however, remained "very depressed".

Visa's net revenue fell 2% to $5.73 billion in the second quarter ended March 31, just higher than analysts' expectations of $5.61 billion, according to the IBES estimate from Refinitiv.

Visa reported net income of $1.38 per Class A share, compared with analysts' estimates of $1.27 per share. (Reporting by Noor Zainab Hussain in Bengaluru; Editing by Devika Syamnath)