A new distinct cultivar of Euphorbia plant named `HJOR045`, characterized by its compact plant habit; very dense and bushy plant form, mainly due to upright stems; large number of long stemmed flowers per plant due to 9 to 14 cm in length reddish peduncles; colored bracts of red, RHS 54B, with an apical margin spot of RHS 138B, green; and large, oblanceolate, yellow-green leaves with reddish-purple margins and abaxial side.