A fifth successive league victory cemented third place for Arsenal in the standings and put the team in good heart for their Champions League last-16 match at Monaco on Wednesday, when they need to overturn a 3-1 deficit from the first leg.
The recalled Giroud fired a shot in off the post in first-half injury time for his 13th goal of the season in all competitions, capping sustained pressure in the opening 45 minutes.
Aaron Ramsey slotted home Giroud's pass for Arsenal's second in the 81st and Mathieu Flamini added another goal in the 84th with one of his first touches after entering as a substitute.
Arsenal have now won eight straight league games at home in a familiar surge in the second half of the season that is trimming the gap to second-place Manchester City in the race for Champions League qualification. Arsenal are six points above fifth-place Liverpool, whose game in hand is at Swansea on Monday.
After a strong start to the season, West Ham are winless in seven league games as they drifts toward mid-table.
With a front four of Giroud, Theo Walcott, Mesut Ozil and Alexis Sanchez, Arsenal played arguably their most exciting attacking lineup for the first time this season and the quartet created chances immediately.
Walcott, who has been out of favor in recent weeks, spurned two decent chances - including one in front of an unguarded net when the ball rebounded out to him off West Ham goalkeeper Adrian.
The Spanish keeper also saved headers from Sanchez and Ramsey, before Giroud took the ball off Ramsey and smashed a left-footed shot that glanced off the post and into the net with seconds left in the half.West Ham enjoyed more possession in the second half and but Arsenal held firm in defense and took their chances late on.
A flowing move ended with Giroud laying off a pass that Ramsey ran onto and steered a rising shot high into the net. Santi Cazorla then rolled an inviting pass along the six-yard box that fellow substitute Flamini gleefully tucked away.Referee Chris Foy went off injured in the second half.
Meanwhile, Aston Villa had taken seven months to score four away goals in this season's Premier League, only to double that amount in the first 45 minutes in a 4-0 win at Sunderland, sparking unrest and a mini-exodus among home fans at half time.
There were also wins for Crystal Palace and West Bromwich Albion.