The last few years have seen Tulane's college baseball team consistently ranked among the best in the nation. The NCAA named it the 17th winningest team of the 2000s in terms of winning percentage and 16th by overall wins.
In 2005 the Green Wave had its best season record in school history, tying its 2001 record for wins. Tulane started the season ranked first in the nation and held the top spot throughout most of the regular season. The Green Wave entered the postseason ranked No. 1 and beat Rice to win its Super Regional. Tulane advanced to the College World Series for the second time in school history. The Green Wave defeated Oregon State 3–1 in its first game but fell 5–0 to Texas, the eventual national champion. In an elimination game against Baylor, the Green Wave led 7–0 in the 7th inning before the Bears scored 8 runs in the final three innings to win the game. Brian Bogusevic won Louisiana Pitcher of the Year, was named to four All-American teams (including Louisville Slugger's first team), and was a semifinalist for three national awards. He was taken in the first round of the 2005 draft by the Houston Astros. Pitcher and first baseman Micah Owings was named Conference USA and Louisiana Player of the Year. He was drafted in the third round by the Arizona Diamondbacks. Third baseman Brad Emaus was named Conference USA and Louisiana Freshman of the Year. Head Coach Rick Jones was named Louisiana Coach of the Year.
In 2006, the Tulane baseball team returned to New Orleans after spending the fall semester at Texas Tech University in Lubbock, Texas due to the effects of Hurricane Katrina. With the renovation of Turchin Stadium delayed, the Green Wave were forced to play home games at nearby Zephyr Field. Despite the distractions and disruptions of their day-to-day lives, the Green Wave finished the regular season 39–17, in third place in C-USA with a 15–9 conference record. Tulane lost to Ole Miss in the NCAA Regionals to end the season.
Prior to the 2007 season the Green Wave was recognized by Baseball America as one of the top college baseball programs in the country since the NCAA expanded its tournament from 48 to 64 teams. The ratings were formulated by evaluating a program's national impact, overall competitiveness, fans and facilities, and academics. The Wave received an "A" rating, one of only 16 teams so designated.
The 2007 season saw the long-term effects of Hurricane Katrina finally wear on the team. With construction underway on the new Turchin Stadium, the Wave played a second straight season at Zephyr Field. A solid 28–11 start to the season (including a sweep of in-state rival LSU) was followed by a 6–15 limp to the finish line. The Green Wave failed to garner an NCAA bid for the first time since 1997.
In 2008 the Green Wave returned to the brand-new Greer Field at Turchin Stadium, built at the site of the old stadium after damage from Katrina scrapped plans for renovations. The stadium features a seating expansion to 5,000 seats, four luxury box suites, a partially covered seating area with 2,700 chairback seats, as well as a new press box. FieldTurf replaced the natural grass surface, and only the mound is made of natural dirt. The Teresa Sofio Hackshack, the team's indoor hitting facility, remains in place next to left field.
The Green Wave have played its home games at Greer Field at Turchin Stadium since 1991. It has a .750 winning percentage in games played there and consistently ranks highly among Division I baseball programs in average attendance figures.