The Europa League tie kicked off 35 minutes late, with the Qarabag team bus caught in heavy traffic, but Dragusin was soon back in the dressing room after dragging Juninho to the ground with the Brazilian through on goal.
Brennan Johnson put Spurs ahead after 12 minutes with his third goal in as many games for Ange Postecoglou's team.
Pape Sarr and newly acquired striker Dominic Solanke struck in the second half, while Toral Bayramov smashed his penalty against the crossbar as the Azerbaijan visitors wasted several gilt-edged chances.
In Istanbul, Turkish giants Fenerbahce, the latest team to be guided by Jose Mourinho, posted a 2-1 home win over Belgian club Union Saint-Gilloise, as both teams finished the game with 10 men.
Defender Caglar Soyuncu opened the scoring for Fenerbahce in the 26th minute with a half-volley from close range before an own goal from Christian Burgess doubled their lead.
Ross Sykes scored in stoppage time for the visitors but it was not enough to stop Mourinho kicking off another European campaign with a victory.
Union defender Kevin Mac Allister received a red card in the 74th minute while Fenerbahce substitute Bright Osayi-Samuel was also sent off in the final minute.
Scottish side Rangers won 2-0 at Malmo with Nedim Bajrami and Ross McCausland scoring, while Roma and Athletic Club drew 1-1.
Lyon beat Olympiacos 2-0 while Ajax thumped Besiktas 4-0.
Former champions Eintracht Frankfurt threw away a two-goal lead in the final minutes as they were held 3-3 by Viktoria Plzen.
As in the Champions League, the traditional group stage of the Europa League has been replaced with an expanded league phase with all 36 teams competing in a single standings.
Each Europa League team will play eight games against eight different opponents through to the end of January.
with PA
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