As others (especially Hubert) have already pointed out, these two sound extremely different for native Germans and there is no way they would be misunderstood (except maybe if a jumbo jet was just taking off next to the two having a conversation, but then nothing can be heard). I would like to give you some guidance on what to listen for to better tell the two apart.
The vowel (diphthong) in deutsch starts with a short-o-like sound to German ears. It is a rather open sound, i.e. well on the way from an average o to an average a. It then rises, closes, unrounds and moves forward to an i-sound (the short German i) in a sound change generally perceived as ‘going upwards’ or ‘closing’. The vowel in durch is not pronounced as a diphthong by all speakers, however it will always start at a very closed, back, rounded u-sound. Depending on how the r is rendered, this will either not move at all or move ‘downward’ (‘opening’). While I would label the sound movement in deutsch as constant motion, in durch the sound would linger on the u before moving and then linger again on the r.
Different dialect speakers may have different starting and ending points for deutsch but they will always move towards closed, i or ü-type vowel. Similarly, different dialect speakers may have a different u sound in durch but it will either not move at all or move towards more open.
The consonant sound at the end of the word is also markedly different in all varieties of German except for a rather small central area. The most obvious difference is in Bavaria, where durch is pronounced with a /x/ sound like Bach. Most other German speakers will use the /ç/ sound as in ich, which is somewhat ‘softer’ and has less rounded lips than the /ʃ/ sound present e.g. in misch — or deutsch. However, these phonemes have merged in a certain central dialect regions in which the words Kirsche and Kirche can no longer be told apart from the (s)ch part alone.
A further tell-tale feature is the fact that deutsch contains an affricate while durch contains a simple fricative. There should be a stop, however weak, separating the diphthong and the /ʃ/ sound in deutsch. On the contrary, the flow of air is not stopped while pronouncing durch.
One final note on recognising homophones in German: except for a few foreign words and the notable exception of ä/e, the vowel letters in German map phonemes rather well. Thus, if a word is spelt with different vowels (and a diphthong shall count as ‘a different vowel’), they will most likely be perceived differently by Germans and not considered homophones or even rhyming.