Getafe squandered a number of chances in the first half before Llorente struck eight minutes after the break with a fine finish from 20 yards.
Partey added a second goal when he tapped in from close range after a counterattack with 10 minutes left.
Getafe had Allan Nyom sent off late on for a high challenge as the defeat dented their bid to secure a Europa League place.
Atleti coach Diego Simeone made six changes to his side as Diego Costa and Yannick Carrasco were both recalled to the starting line-up.
With an entirely new back four, Atleti's defence looked vulnerable and they were fortunate not to be behind at the break after an impressive first-half display from Getafe.
Jaime Mata had three good chances in quick succession early on as he lifted a shot over the bar, saw an effort hooked off the line by Felipe and miscued a close-range shot.
Atleti's best opportunity before the interval fell to Costa after he got on the end of Llorente's cross, but the striker could only guide his header over the crossbar.
The same combination linked up again three minutes into the second half, but Costa failed to hit the target from a central position following Llorente's cut back.
Llorente took matters into his own hands shortly afterwards when he smartly turned Getafe's David Timor on the edge of the box then wrong-footed goalkeeper David Soria with a low shot into the corner.
Partey made the points safe when he confidently guided the ball home after Getafe were caught on the break, and the home side then saw Nyom sent off in stoppage time.
What does it mean? Atletico edge closer to third
With Champions League football already assured for both, Atleti are jostling with Sevilla to finish in third spot.
This victory gave Simeone's side a two-point cushion over Sevilla – who drew 0-0 at Real Sociedad – meaning they are well-placed to achieve their target.
Getafe are clinging on to the final Europa League spot in LaLiga after this defeat.
Llorente stars up front
Originally a bustling central midfielder, the former Real Madrid man has been reinvented as a versatile attacker by Simeone, and he oozed class against Getafe. Llorente was Atleti's most creative player with intelligent movement and capped a fine display with a well-taken goal.
Mata fails to make his mark
The Getafe striker escaped the attentions of Atleti's defence and frequently found himself in dangerous goalscoring positions, but all too often his poor finishing or a lapse in concentration let him down at the key moment.
Atleti host Real Sociedad in their final LaLiga fixture of the season on Sunday, while Getafe travel to Levante.