ODI career
He made his ODI debut on 14 April 1994 against Sri Lanka in the 1994 Austral-Asia Cup at Sharjah and was not required to bat, as Australia chased down 155 comfortably with nine wickets to spare. By the 1995–96 season, he became a regular in the team. He proved a reliable anchor at the bottom of the middle order, and he would often patiently guide Australia to victory following a rare top-order collapse – leading to him being nicknamed "The Finisher". By the end of his ODI career, Bevan was known as the "Pyjama Picasso". During his ODI career, he managed to hit just 21 sixes in 232 ODI matches, a testament to his calculating style and batting role that required protecting his vital wicket rather than attempting risky aerial shots. He batted 45 times in successful ODI run chases for Australia; and, out of those 45 outings, he remained unbeaten at the crease on 25 occasions.
One of his most famous "anchor" innings was in the New Year's Day One Day International at the Sydney Cricket Ground against the West Indies in 1996 during the Benson & Hedges World Series. With the Australians at one stage 6/38 chasing 173, his unbeaten 150-minute 78 got the Australians over the line with a four or more required on the last ball to achieve victory. He was the second leading run scorer in the 1995/96 Benson & Hedges World Series only behind Mark Taylor with an aggregate of 389 runs in 10 innings at an average of 194.50, bolstered by eight not-outs in his 10 innings.
He featured in his first World Cup tournament during the 1996 Cricket World Cup and played a crucial role to help Australia to reach the final of the tournament by scoring 69 runs in the semi-final clash against the West Indies, a match which is highly remembered and known due to the dramatic collapse of the West Indies in a low-scoring run chase of 208. He also played an important cameo of unbeaten 36 off 49 balls in the 1996 World Cup final which propelled Australia to a decent total of 241/7 on the board. However, his efforts went in vain as Sri Lanka chased down 242 to win their maiden World Cup title.
He was selected to the Australian squad for the 50-over cricket tournament at the 1998 Commonwealth Games where Australia became runners-up in the competition to South Africa. He was a key member of the Australian team which lifted the 1999 Cricket World Cup.
On 8 April 2000, he played arguably the best knock of his career where he steered the mammoth epic run chase of 321 by scoring an unbeaten 185 off just 132 deliveries in an unofficial ODI held in Dhaka which almost guaranteed Rest of the World XI for an unlikely victory against the Asia XI. Rest of the World XI at one stage were reeling at 7/196 in the 37th over and was staring at a big defeat before Bevan came to the rescue who smashed 19 fours and five sixes to provide a glimmer of hope. He alongside Andy Caddick put on a 119 run partnership for the eighth wicket which led to a great recovery for the chasing team. However, Rest of the World XI lost by just one run in the end despite the heroics of Bevan. Caddick was involved in a brain-fade moment in the critical juncture of the match as he was run out on the penultimate delivery effectively denying Rest of the World XI a famous win given the circumstances on how the game had panned out. However, his knock of 185 not out could not be realised as Bevan's highest ODI or even List A score due to the fact that the match did not have any status as it was deemed as an unofficial ODI meaning the match does not even count as a List A match.
In January 2002, he scored a crucial unbeaten 95 ball 102 in a match against New Zealand in a modest run chase of 246 at the iconic Melbourne Cricket Ground. He arrived to the crease as he once again had to do the bulk of scoring runs after a top-order collapse leaving Australia were reeling at 82/6 at one point and later 143/7. His knock guaranteed Australia a thrilling two wicket win over New Zealand with three balls to spare.
Bevan entered the 2003 Cricket World Cup injured. He played his first game in the group stage against India. He didn't bat until the fifth group game against Namibia and he registered a rusty 17 before being caught and bowled by Louis Burger. In the final group game against England, he came in with Australia struggling at 48–4. He then was joined by Andy Bichel at 135–8 with 70 runs still required to win. Bevan finished on 74 not out and Bichel 34 not out as Australia won in the final over. An unbeaten group stage was followed by an unbeaten Super Six stage. He made 56 against New Zealand helping Australia recover from 84–7 again batting with Bichel to help Australia win. His last knock was an unfortunate golden duck in the semi-final against Sri Lanka and he was not required to bat in the final which Australia won.