The table below shows some stats for their pitching staff in the first half vs. the second half, with data coming from Baseball Reference. The numbers in the 2nd part of the table are all rates, with the stat being divided by PA.
Notice that their SO/BB ratio fell by 19%. If someone told you that this would happen, my guess is that you would have thought it would be bad news for the Twins. You can see that their SO rate is down and their BB rate is up (for those rates, I included HBP and IBBs in the rate). They have also allowed a higher single rate.
But there are big drop offs in 2Bs and HRs. A 45% drop in HR rate seems very large. They allowed 92 HRs in 88 games before the All-Star break and 33 in 57 games since the break. AVG and OBP did not change much. But SLG did, probably due to the lower rate on 2Bs and HRs (of course, fewer 2Bs might be the result of better fielding).
I don't know why the HR rate fell. Maybe more games at home, the opposition, the flyball rate, etc. Those are all just speculation.
The starters saw their AVG-OBP-SLG go from .282-.321-.454 to .252-.302-.362. A 92 point drop in SLG! But, the relievers saw the following change: .237-.296-.378 to .278-.339-.395. The starters saw their OPS fall .111 while the relievers had a .060 gain! In the 1st half, the starters faced 69.3% of the batters while in the 2nd it was 69.8%. So, although the relievers did worse and pitched the same relative amount in the 2nd half, the better performance all comes from the starters (although Duensing changed roles, becoming a starter).