A storming second-half comeback earned Wexford another precious Leinster Championship point in Pearse Stadium, though they left the West knowing it could have been so much better.
Seven unanswered points between the 50th and 63rd minutes gave Davy Fitzgerald's men a lead for the first time all day, but they couldn't close the deal, Cathal Dunbar's mis-hitting a late goal chance that allowed Galway goalkeeper, Colm Callanan save and clear.
Fitzgerald was ordered into the stand after an angry 44th minute confrontation with a fourth official, yet all the late momentum was Wexford's and they were left to rue not taking an opportunity to beat a Galway side clearly still feeling the absence of Joe Canning.
Galway led 0-6 to 0-0 before Chin opened Wexford's account in the 22nd minute. Nolan quickly added his score and two more Chin points from placed balls brought Wexford to within four points with just three minutes of the half remaining.
Galway closed out stronger, though, scores from Conor Cooney and Whelan easing them to that advantage of six at the mid-point.
Galway's 41st minute introduction of Johnny Glynn gave them a valuable puck- out target and they looked to be easing to a humdrum victory when leading 0-14 to 0-8 with 20 minutes of normal time remaining.
But Wexford came storming back with that late surge and will regret their massive accumulation of 16 wides on a day the Westerners were undoubtedly there for the taking.
After the game, Fitzgerald insisted he could never be happy in failing to win.
"I go out to win hurling games," he said. "That is very important to me. But what I'm happy with is the manner in which our lads fought. I thought it was incredible.
"We missed a lot of easy scores out there today. We still kept going. If you're involved with any team then that is what you want."
Fitzgerald insisted it wasn't a first-time offence against his corner-back. "It is the second time we have played here and Damien Reck has been taken out off the ball twice," he said.
"I didn't abuse him, but I said that is not acceptable because it led to a point."
SCORERS: Galway: J Flynn 0-6 (3 fs, 65), N Burke 0-4 (3 fs, '65'), C Whelan 0-3, David Burke, C Mannion and C Cooney 0-1 each. Wexford: L Chin 0-7 (6 fs, 65), R O'Connor, C Dunbar 0-2 each, S Murphy, A Nolan, C McDonald, D O'Keeffe, L Og McGovern 0-1 each.