Rick Porcello (11-6) allowed two runs and five hits in eight innings, striking out six.
Tyler Chatwood (6-7) gave up six runs on eight hits and two walks in 5 1-3 innings. The Angels had won three straight and five of seven.
With one out in the sixth, Martinez gave the Tigers a 3-2 lead with an RBI single, and Guillen followed with his first triple since July 9, 2010. Alex Avila drove in Guillen with a base hit, ending Chatwood's night and putting Detroit up 6-2.
Martinez and Guillen added RBI doubles in the seventh to give the Tigers a six-run lead, and the pair both drove in runs for the third straight inning in Detroit's three-run eighth.
The teams traded solo homers in the first, with Maicer Izturis' leadoff shot being matched by Brennan Boesch's 418-footer. The Angels went ahead again in the fifth on Mark Trumbo's double — his sixth RBI in two days — but Detroit made it 2-2 in the bottom of the inning on Santiago's RBI double.
NOTES: Angels shortstop Erick Aybar made a highlight-reel play to start a 6-4-3 double play in the fourth. A bad hop bounced off his chest, but he reached down and swatted the ball with his bare hard to Izturis, who made the relay throw to first. ... Howie Kendrick lost control of his bat in spectacular fashion in the fifth inning, with it landing in the stands past third base. On the next pitch, he lined a pitch into his own dugout. No one was injured on either play. ... Austin Jackson is on pace for 177 strikeouts, which would break his own major league record for players hitting fewer than 10 homers in a season. Jackson struck out 170 times as a rookie last season.