City made the most of Chelsea and Arsenal both playing in the Champions League semi-finals this weekend to move up to 41 points, three behind leaders Manchester United and one ahead of the Blues.
With 17 of their 22 league games played, Arsenal are fourth on 38 points with a game in hand over the two Manchester clubs, while Chelsea have two games in hand over the top two.
Kelly set the tone with two quick goals before WSL top scorer Shaw netted in the second half and defender Steph Houghton (35) scored on her birthday as the Hammers were outclassed in the rain in Manchester.
Earlier in the day, Rachel Daly (31) struck in the 84th minute to snatch a 3-3 draw for Aston Villa away to Tottenham Hotspur following a thrilling game in which the visitors led 2-0 before Spurs came roaring back to go 3-2 up.
Eveliina Summanen (24) pulled a goal back before the break and added a second early in the second half before Bethany England gave them the lead, but Daly headed her 15th goal of the season to grab a share of the points for the visitors.
Relegation-threatened Reading threw away a two-goal lead as they lost 3-2 at home to Everton to leave them in 11th place in the 12-team league on 11 points, one more than bottom side Leicester City, who have a game in hand.
Elisabeth Terland (21) netted her third goal in two WSL games for Brighton & Hove Albion against Liverpool, but two strikes from Ceri Holland (25) saw the Reds run out 2-1 winners and leave the struggling Seagulls in 10th place on 12 points.
