A right arm offspinner, Suraj had a successful under-age career in Sri Lanka. He represented his country at under-15 and under-19 level and took 23 wickets in four matches at an Under-23 tournament of 2003-04. This effort caught the attention of Marvan Atapattu, who was influential in getting him over to Sinhalese Sports Club. He went on play for Sri Lanka A and Sri Lanka.
In December 2009, he replaced Muttiah Muralitharan in Sri Lanka's ODI squad in India and he made his debut in the second match of the series in Nagpur. He impressed by taking three wickets for 51 runs; Sri Lanka went on to win the match by three wickets.
On 16 August 2010, in an incident that drew considerable media attention, Randiv intentionally bowled a no ball—overstepping the bowling mark by a significant margin—to Virender Sehwag—then on 99—that ensured a victory for India in the ODI, while denying Sehwag a chance to score a century. Sehwag hit the ball for six but as the winning run was registered as soon as the umpire signalled no ball, Sehwag's shot was deemed to have been made after the end of the match. Randiv later apologised to Sehwag for use of the tactic; he was docked his match fees for the game and handed a one match suspension by Sri Lanka Cricket.
He was omitted from Sri Lanka's squad for the 2011 Cricket World Cup, but was called up as a replacement for the injured Angelo Mathews, and was subsequently picked for the World Cup Final.