French midfielder Amalfitano opened the scoring in the 21st minute before Senegalese striker Sakho, who joined from Metz in the summer, made it six goals in as many matches with 15 minutes remaining.
Silva pulled one back for City two minutes later but were unable to create an equaliser as Sam Allardyce's men cemented their spot in the top four with a third straight win as Manuel Pellegrini's side remained five points behind league leaders Chelsea who take on Manchester United on Sunday.
The Chilean netted on the half-hour mark and in injury-time to guide the Gunners to a third triumph of the campaign which has them placed fifth on the table, two points out of the top four.
Brede Hangeland's second goal for the Eagles and captain Mile Jedinak's stoppage time penalty had Neil Warnock's side in pole position before the Baggies hit back through Victor Anichebe prior to Saido Berahino's injury-time conversion from the spot which yielded his seventh goal of the term.
Second-placed Southampton moved to within three points of Chelsea with a narrow 1-0 win over Stoke City at St Mary's which came courtesy of Sadio Mane's second of the season while Hull City held Liverpool to a 0-0 draw at Anfield to move into the top half of the table.
Monday night's clash pits bottom-placed QPR against Aston Villa at Loftus Road.
2014/15 Barclays Premier League - season scores
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