This year's edition broke the record of the 1969 team, which had gotten 262 of its 1,124 whiffs out of the bullpen, or 23 percent.
On the 2012 staff, relievers contributed 437 strikeouts toward the record that stood at 1,127 by the end of Tuesday's game. That's 39 percent.
Among the 1969 relievers, Bruce Del Canton's 56 strikeouts were a team high. Both Grilli (85) and Joel Hanrahan (67) already have more.
Grilli was quick to acknowledge the contribution of the middle of the bullpen.
"I give a lot of props to guys like [Chris] Resop and [Jared] Hughes and [Tony] Watson," Grilli said. "They don't get enough credit for what they do, make really tough pitches in tough situations. They really set the stage."