Deduno (6-4) overcame five walks en route to the decision, allowing two runs on four hits while striking out five.
The Twins right-hander exited with a 4-2 lead but the Angels mounted a rally in the eighth.
Closer Glen Perkins entered only to yield a run-scoring single to pinch hitter Collin Cowgill.
That brought up another pinch-hitter, Chris Iannetta, who blasted a Perkins delivery deep into left. The ball seemed headed over the fence for a three-run homer but Thomas leaped to haul it back, preserving Minnesota's lead.
Perkins finished with a scoreless ninth for his 24h save and Thomas went 2-for-4 with a solo homer and two RBI as the Twins took the first contest of a seven-game West Coast road trip.
Angels starter Joe Blanton (2-13) lasted just 3 2/3 innings, coughing up four runs on nine hits.
Kendrick and Mike Trout each supplied an RBI for Los Angeles.
Celebrity Families of 2014 [PHOTOS]