The 29-year-old United States international arrived at Ewood Park in a loan deal from Schalke until the end of the season and was thrown straight into the action at left back.
Jones was made available for transfer by the Bundesliga side after three-and-a-half injury-plagued years but adjusted to the pace of the English game straight away and was influential both at the back and going forward.
Rovers boss Kean said: "He's not even fully fit. He has not played for a number of weeks but he's got everything. I tried to say to him at the end, 'just save your legs a little bit', but he finds that difficult, he wants to tackle and join in.
"His passing and the way he kept the ball for us as well was fantastic. He was a £10 million player before his last injury and, with his performance today and another couple of games under his belt, I think he'll be fantastic for us.''
Blackburn's new owners Venky's have stated their desire for a marquee signing before the January transfer window closes, but so far only Jones and fellow loan signing Roque Santa Cruz, who also played 90 minutes yesterday, have arrived at Ewood Park.
Kean revealed on Friday he had turned his attentions to Argentinian playmaker Mauro Formica of Newell's Old Boys but he admitted that is far from a done deal.
"It's been a little bit frustrating,'' he said. "We had a bid for Seb Larsson and he's now not available so we'll respect Birmingham's decision and we move on.''
Of Formica, he added: "That's gone a little bit quiet so I'm not really sure where we're at. That'll be picked up today again and we'll see where we are with that.''
On the pitch, things could scarcely be going better for Kean, though, and, with a number of players returning from injury, the Rovers boss is able to look forward with optimism whatever happens this month.
He said: "We don't need too many (signings) and the good thing is we've got Steven Nzonzi back on the pitch and we've also got Vince Grella and Keith Andrews back on the training ground this week so competition for places is hotting up, which will give me another problem.''
West Brom had hoped to build on last week's win over Blackpool, which ended a run of six straight losses, but instead they shot themselves in the foot when Gabriel Tamas headed an own goal in the 41st minute, with Junior Hoilett adding a fine second less than two minutes after half-time.
The incident that really riled Baggies boss Roberto Di Matteo, however, was a foul by Jones on Peter Odemwingie in the 68th minute for which referee Mark Clattenburg awarded a free-kick despite the incident appearing to occur at least a yard inside the box.
He said: "I think, apart from the referee, everybody else thought we should have had a penalty. It's a foul and it's a penalty and I don't know how he saw it outside the box.''