Barcelona suffered a surprise loss at Granada earlier in the day, meaning Real – who went second in the table with the win – pulled level on points with city rivals Atletico Madrid, who visit Getafe on Sunday.
Star man Cristiano Ronaldo was once again sidelined with a knee injury but it did not hamper Real, who made light of the Portuguese star's absence.
Angel Di Maria scored a 28th-minute opener for Real, and he and Gareth Bale, who scored just after the break, both played starring roles in the victory that extended Almeria's losing run on the road to eight matches.
Isco and Alvaro Morata wrapped up the win with further second-half goals as Real breathed life into their title bid, despite consecutive defeats to Barcelona and Sevilla late last month.
Almeria forward Jonathan Sundy Zongo headed over from an early corner but Real soon hit their stride as Di Maria thudded a 25-yard drive against the crossbar in the fifth minute.
Di Maria seemed determined to find the scoresheet in memorable fashion and Almeria goalkeeper Esteban Suarez saved well as the midfielder struck twice more from outside the penalty area in quick succession.
Karim Benzema lofted a shot over from Bale's 12th-minute cut-back on the end of a blistering run down the left flank.
Bale opted to go it alone midway through the half, cutting in past a pair of challenges to draw another fine save from Esteban, but Di Maria would eventually have his ambition rewarded.
The Argentina midfielder exchanged passes with Nacho to engineer space in the box and arrowed an angled left-footed shot into the far left-corner.
A tangle between Zongo and Fabio Coentrao in the Almeria penalty area then went unpunished by referee Juan Martinez before Bale and Benzema shot wide in the closing moments of a half where the scoreline flattered Francisco's team.
Bale doubled Real's lead eight minutes into the second half, drilling low past Esteban after Benzema and Di Maria linked smoothly.
Benzema was involved again three minutes later, sending a searching cross from the right for Isco to control and whip past Esteban at his near post.
Coentrao was denied a fourth by Esteban, while Benzema failed to adjust his feet in time to convert Nacho's cross and claim the goal his endeavours deserved.
Real Madrid coach Carlo Ancelotti removed Bale with 20 minutes remaining to allow Morata's productive cameo, not wishing to compound a lengthy absentee list that also included Sami Khedira, Jese, Alvaro Arbeloa and Marcelo.
And Morata converted a lifted pass from Asier Illarramendi to complete the scoring with five minutes left, sealing a win that put the pressure on Atletico.
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