Chavez fanned Kevin Youkilis and Wells with two on to end the 13th, then Travis Hafner and Wells in the 15th.
Jerry Blevins escaped a bases-loaded jam in the top of the 11th with two strikeouts. Pat Neshek worked out of trouble with runners on first and second in the 12th.
Robinson Cano hit a two-run homer in the first as New York ended a season-long five-game stretch without a long ball, but the Yankees didn't score again on another day of missed opportunities.
"I think it's probably a little more frustrating because you can look at how you had an opportunity here and an opportunity there," manager Joe Girardi said. "A lot of guys probably look at that, but it doesn't change the result."
It was the longest day game in Coliseum history.
Neither A' starter Jarrod Parker nor New York counterpart Hiroki Kuroda got a decision after a nice pitchers' duel hours before the game ended.
After Smith's tying, two-out double in the third, Oakland didn't reach base again until Jaso's bloop single leading off the ninth.
Oakland won the season series 5-1 for its second-best mark against the Yankees in franchise history. The 1990 club went 12-0.
The A's tied it at 2 in the third on a close play at the plate. Smith doubled off the wall in right and the relay throw was on target to Stewart, who tagged Jaso with his glove but had the ball in his bare hand.
Jaso was called safe by plate umpire CB Bucknor, drawing an argument from Girardi.
Earlier in the inning, Derek Norris' RBI groundout scored Chris Young, who drew a leadoff walk. Eric Sogard followed with a single before the A's pulled off a double steal.
Parker, riding a three-start winning streak, was helped by a pair of double plays in the first four innings.
Kuroda's winless stretch reached five starts since he beat Toronto on May 17. He became the third Japanese-born pitcher with 1,000 innings in the majors, joining Hideo Nomo and Tomo Ohka.
Girardi bumped Jayson Nix up to the No. 2 spot in the batting order from eighth a night earlier to shake things up and get the Yankees going, but Nix went 1 for 5 with a strikeout to end the 12th.
NOTES: Yankees captain Derek Jeter had his surgically repaired left ankle examined by Dr. Robert Anderson in Charlotte, N.C., and was cleared to resume baseball activities and running. ... Crisp (bruised heel) and LF Yoenis Cespedes (tight left hamstring) were held out of the starting lineup. ... Rivera received a surfboard and a bottle of white wine from Napa Valley from the A's in a pregame ceremony, along with a $10,042 donation to his foundation. ... The A's are 7-0-2 in their last nine series. ... New York agreed to contract terms with Notre Dame 3B Eric Jagielo, who signed for $1,839,400. He was the 26th overall pick in last week's draft and one of three first-round selections by the Yankees.