The promotion-chasing Hammers, backed by over 6,300 travelling supporters - their largest following since 2004 - were seriously tested in an entertaining, albeit occasionally niggly, encounter which was much closer than the second-tier table would have suggested.
City, second-bottom with only two wins to their name all season, took a deserved lead into half-time courtesy of Clive Platt's well-taken turn and finish.
Carlton Cole stepped off the bench at the break and, much to the relief of the packed away end, duly pulled the Hammers level in the 69th minute having latched on to Robert Green's long kick.
And Frederic Piquionne ensured West Ham kept up the pressure on leaders Southampton when he somehow converted Julien Faubert's cross just six minutes later to cap an improved second-half display.
Jack Collison lodged his contender for miss of the season in injury time but it mattered little as West Ham took all three points.
Sam Allardyce named an unchanged Hammers XI from the side who won 2-0 at Hull prior to the international break.
Fit-again Coventry duo Martin Cranie and Chris Hussey returned to Coventry's starting line-up along with rookie midfielder Gael Bigirimana, upon completion of his three-match suspension, and the recalled Platt.
The hosts showed no signs of intimidation inside the opening exchanges, with both sides contributing towards a free-flowing encounter played at pace.
In fact, it was Coventry who dominated possession in the first quarter and they went on to deservedly break the deadlock in the 33rd minute, full-back Cyrus Christie sending in a low cross from the right which Platt did well to control, turn on and fire home from 12 yards.
City went close to doubling their lead through Platt's header before Gary McSheffrey was denied by some last-ditch Hammers defending as he launched himself at the ball, with the hosts given a standing ovation by their supporters at the interval.
Allardyce turned to Cole at half-time and the substitute entered proceedings with the tempo of the encounter continuing where it had left off.
McSheffrey and Lukas Jutkiewicz tried their luck from distance for the Sky Blues, the latter being denied by a super parried save from Green.
The outcome was anything but certain as the game continued to flow from end to end, with the Hammers starting to take a hold.
And it was they who drew level in the 69th minute through Cole, who latched on to Green's long kick upfield, shrugged off the attention of Richard Keogh and fired past Joe Murphy.
The turnaround was soon complete as Faubert sent over a cross from the right and Piquionne, somehow, connected with the ball at the back post and beat Murphy.
Coventry rallied in search of an equaliser, Platt heading wide before Conor Thomas and Sammy Clingan both saw efforts blocked by Kevin Nolan.
Collison was then presented with the simplest of chances to wrap matters up in added time but he could only fire over from six yards, although it proved inconsequential.